MAT 105 AD2 College Algebra
A can has a surface area of 901 square inches. Its height is 6.59 inches. What is the radius of the circular top? Use 3.14159 for π. Round to the nearest hundredth. A. 9.12 in B. 21.76 in C. 4.35 in D. 11.58 in
A. 9.12 in
Graph the solution set. |x|≤5 A. [-5 to 5] B. (-5 to 5) C. ) -5 to 5 ( D. ] -5 to 5 [
A. [-5 to 5]
Solve for y. 7=10x−7y A. y=10x−7/7 B. y=14+10x C. y=14−10x D. y=10x+7/7
A. y=(10x-7)/7
Graph the following polynomial equation. f(x)=2x^3(x^2−4)(x−4) Which of the following graphs correctly matches the graph of f(x)? A. -55-36040xy A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 360 to 40 in increments of 40. From left to right comma a curve rises in quadrant 3 comma is horizontal when passing through the origin comma rises to a maximum in quadrant 1 comma falls to a minimum 4 units to the right of the origin comma and rises in quadrant 1. B. A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 360 to 40 in increments of 40. From left to right, a curve falls and passes through a point 2 units to the left of the origin to a minimum in quadrant 3, rises and is horizontal when passing through the origin to a maximum in quadrant 1, falls and passes through a point 2 units to the right of the origin to a minimum in quadrant 4, and rises passing through a point 4 units to the right of the origin into quadrant 1. Your answer is correct. C. -55-36040xy A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 360 to 40 in increments of 40. From left to right, a curve rises in quadrant 3 passing through a point 4 units to the left of the origin to a maximum in quadrant 2, falls and passes through a point 2 units to the left of the origin to a minimum in quadrant 3, rises and is horizontal when passing through the origin, rises to a maximum in quadrant 1, falls and passes through a point 2 units to the right of the origin into quadrant 4. D. -55-36040xy
B. A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 360 to 40 in increments of 40. From left to right, a curve falls and passes through a point 2 units to the left of the origin to a minimum in quadrant 3, rises and is horizontal when passing through the origin to a maximum in quadrant 1, falls and passes through a point 2 units to the right of the origin to a minimum in quadrant 4, and rises passing through a point 4 units to the right of the origin into quadrant 1. Your answer is correct. Small hump, long hump (negative)
Walt made an extra $9,000 last year from a part-time job. He invested part of the money at 7% and the rest at 8%. He made a total of $680 in interest. How much was invested at 8%? A. $7,000 B. $5,000 C. $4,500 D. $4,000
B. $5,000
{NOT EDITED} Find a polynomial of degree 3 with only real coefficients and zeros of −4, 2, and 0 for which f(−1)=−1. Choose the correct polynomial of degree 3 with only real coefficients and zeros of −4, 2, and 0 for which f(−1)=−1. A. f(x)=−116x3−916x3+116x3 B. {EDITED} f(x)=−1/9x^3−2/9x^2+8/9x C. f(x)=19x3+29x2−89x D. f(x)= who cares, it's not this one!
B. {EDITED} f(x)=−1/9x^3−2/9x^2+8/9x
Suppose the point (2,4) is on the graph of y=f(x). Find a point on the graph of the given function. y=4f(x) A. (5,3) B. (8,4) C. (2,16) D. (3,8)
C. (2,16)
Determine the intervals over which the function is decreasing, increasing, and constant. {A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A V-shaped graph that opens downward has vertex (negative 5, 0) and passes through the points (negative 6, negative 1) and (negative 4, negative 1).} A. The function is decreasing on (−∞,−5], constant on [−5,5], and increasing on [5,∞). B. The function is decreasing on (−∞,−5] and increasing on [−5,∞). It is never constant. C. The function is increasing on (−∞,−5] and decreasing on [−5,∞). It is never constant. D. The function is increasing on (−∞,−5], constant on [−5,5], and decreasing on [5,∞).
C. The function is increasing on (−∞,−5] and decreasing on [−5,∞). It is never constant.
Find the slope and the y-intercept of the line. x+5y=−3 A. The slope is −5, and the y-intercept is −3. B. The slope is 1/5, and the y-intercept is −3/5. C. The slope is −1/5, and the y-intercept is −3/5. Your answer is correct. D. The slope is −3/5, and the y-intercept is −1/5.
C. The slope is −1/5, and the y-intercept is −3/5. Your answer is correct.
Solve the equation. 2x+8/2−2x/x−2=x A. {−2/3} B. {4/3} C. {4} D. {2}
C. {4}
Describe the end behavior of the graph of the polynomial function. f(x)=3x^6−5x^4+x^2−2 Choose the correct answer below. A. A figure shows two curved arrows. The arrow on the left starts in the middle of the figure and curves upward in a clockwise direction. The arrow on the right starts in the middle of the figure and curves downward in a clockwise direction. B. A figure shows two curved arrows. The arrow on the left starts in the middle of the figure and curves downward in a counterclockwise direction. The arrow on the right starts in the middle of the figure and curves upward in a counterclockwise direction. C. A figure shows two curved arrows. The arrow on the left starts at the top of the figure and curves downward in a counterclockwise direction. The arrow on the right starts at the top of the figure and curves downward in a clockwise direction. D. A figure shows two curved arrows. The arrow on the left starts at the bottom of the figure and curves upward in a clockwise direction. The arrow on the right starts at the bottom of the figure and curves upward in a counterclockwise direction. Simply: up; up
D. A figure shows two curved arrows. The arrow on the left starts at the bottom of the figure and curves upward in a clockwise direction. The arrow on the right starts at the bottom of the figure and curves upward in a counterclockwise direction. Simply: up; up
{NOT EDITED} Which one of the graphs is that of y=x3−8x2−16x+128? Choose the correct answer below. A. -1010-125125xy A coordinate plane has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 125 to 125 in increments of 25. From left to right, a function falls at a decreasing rate, crossing the y-axis at (0,17), then crossing the x-axis from above at (1, 0). It flattens out until about x equals 5, and then falls at an increasing rate. B. -1010-125125xy A coordinate plane has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 125 to 125 in increments of 25. From left to right, a function falls at a decreasing rate, touching the x-axis from above at (negative 5, 0) and turning back upwards, then falls, crossing the x-axis at the origin, then rises again at an increasing rate, crossing the x-axis at (3, 0). C. -1010-60003000xy A coordinate plane has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 6000 to 3000 in increments of 500. From left to right, a function falls at a decreasing rate, crossing the x-axis from above at (negative 4,0), then rises, touching the x-axis from below at (negative 1,0) and turning back downwards, then rises, crossing the x-axis at (3,0), and finally falls at an increasing rate, crossing the x-axis at (3,0). D. -1010-200250xy
D. The answer is a swavy line.
From April through December 2000, the stock price of a company had a roller coaster ride. The table below indicates the price of the stock (in dollars) at the beginning of each month during that period. Find the average rate of change in price per month between June and September. Round to the nearest cent as needed. Month ~ Price April ~ 115 May ~ 108 June ~ 89 July ~ 101 August ~ 94 September ~ 112 October ~ 92 November ~ 85 December ~ 64 A. $11.50 per month B. −$11.50 per month C. −$7.67 per month D. $7.67 per month
D. $7.67 per month
Decide whether the statement is true or false. −6 is a solution of −2x+3=17. True False
False
Find the requested value. f(4) for f(x)= {2x+6,if x≤0, 2−3x,if 0<x<3, x,if x≥3 A. 4 B. −10 C. 3 D. 14
A. 4
Find f(−2) when f(x)=x^2+5x+4. A. −10 B. −2 C. 10 D. 18
B. -2
Find the slope of the line that passes through the points (−3,−6) and (−2,−4). A. 12 B. −2 C. 2 D. -1/2
C. 2
A square plywood platform has a perimeter which is 7 times the length of a side, decreased by 12. Find the length of a side. A. 3 B. 1 C. 4 D. 7
C. 4
Write an equation for the line that passes through the point (2,−1) and that has a slope of −3. Give your answer in slope-intercept form. A. y=3x+5 B. y=3x−5 C. y=−3x+5 D. y=−3x−5
C. y=−3x+5
Solve the equation. squ. root (3x+10) = 5−2x A. {5/4,9} B. {3/4,5} C. {3/4} D. {5}
C. {3/4}
Find the center-radius form of the equation of the circle with center (8,2) and radius 12. A. (x−2)^2+(y−8)^2=12 B. (x+8)^2+(y+2)^2=144 C. (x+2)^2+(y+8)^2=12 D. (x−8)^2+(y−2)^2=144
D. (x−8)^2+(y−2)^2=144
Solve the equation. 4[4x+6+6(x+1)]=−3x+7 A. −41/4 B. 7/43 C. 7/4 D. −41/43
D. -41/43
Find the slope of the line that passes through the points (−2,−8) and (8,−3). A. 2 B. −2 C. −12 D. 1/2
D. 1/2
Solve the equation. 1−9/5x=10/9 A. {−9} B. {81} C. −81/5 D. 81/5
D. 81/5
{NOT EDITED} Graph the function. g(x)=−(x−3)3−2 A. -1010-1010xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. From left to right, a curve falls at a decreasing rate passing through the point (2, negative 1), is horizontal when passing through the point (3, negative 2), and falls at an increasing rate, passing through the point (4, negative 3). B. -1010-1010xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. From left to right, a curve rises at a decreasing rate passing through the point (2, negative 3), is horizontal when passing through the point (3, negative 2), and rises at an increasing rate, passing through the point (4, negative 1). C. -1010-1010xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. From left to right, a curve falls at a decreasing rate passing through the point (2, 3), is horizontal when passing through the point (3, 2), and falls at an increasing rate, passing through the point (4, 1). D. -1010-1010xy
A. -1010-1010xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. From left to right, a curve falls at a decreasing rate passing through the point (2, negative 1), is horizontal when passing through the point (3, negative 2), and falls at an increasing rate, passing through the point (4, negative 3).
Describe the end behavior of the graph of the polynomial function. f(x)=−5x^3+2x^2−1 Choose the correct answer below. A. A figure shows two curved arrows. The arrow on the left starts in the middle of the figure and curves upward in a clockwise direction. The arrow on the right starts in the middle of the figure and curves downward in a clockwise direction. Simply: up; down B. A figure shows two curved arrows. The arrow on the left starts in the middle of the figure and curves downward in a counterclockwise direction. The arrow on the right starts in the middle of the figure and curves upward in a counterclockwise direction. C. A figure shows two curved arrows. The arrow on the left starts at the top of the figure and curves downward in a counterclockwise direction. The arrow on the right starts at the top of the figure and curves downward in a clockwise direction. D. A figure shows two curved arrows. The arrow on the left starts at the bottom of the figure and curves upward in a clockwise direction. The arrow on the right starts at the bottom of the figure and curves upward in a counterclockwise direction.
A. A figure shows two curved arrows. The arrow on the left starts in the middle of the figure and curves upward in a clockwise direction. The arrow on the right starts in the middle of the figure and curves downward in a clockwise direction. Simply: up; down
Q.53 Find the domain and range of the rational function graphed below. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A graph has two branches. A horizontal asymptote crosses the y-axis at 3 and a vertical asymptote crosses the x-axis at negative 4. The first branch is above the horizontal asymptote and to the left of the vertical asymptote, approaching both. The second branch is below the horizontal asymptote and to the right of the vertical asymptote, approaching both. A. Domain: (−∞, −4) ∪ (−4, ∞) Range: (−∞, 3) ∪ (3, ∞) Your answer is correct. B. Domain: (−∞, ∞) Range: (−∞, 3) ∪ (3, ∞) C. Domain: (−∞, −4) ∪ (−4, ∞) Range: (−∞, ∞) D. Domain: (−∞, 3) ∪ (3, ∞) Range: (−∞, −4) ∪ (−4, ∞)
A. Domain: (−∞, −4) ∪ (−4, ∞) Range: (−∞, 3) ∪ (3, ∞)
Use the equation and the corresponding graph for the quadratic function to find the domain and range. f(x)=(x−3)^2−2 A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (3, negative 2) and passes through the points (2, negative 1) and (4, negative 1). A. Domain: (−∞,∞); Range: [−2,∞) B. Domain: [−2,∞); Range: (−∞,∞) C. Domain: (−2,∞); Range: [2,∞) D. Domain: (−∞,∞); Range: (−∞,−2]
A. Domain: (−∞,∞); Range: [−2,∞)
Find the horizontal and vertical asymptotes of the rational function graphed below. -10-8-6-4-2246810-10-8-6-4-2246810xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A horizontal asymptote crosses the vertical axis at y=4 and a vertical asymptote crosses the horizontal axis at x=negative 3. A graph has two branches. The first branch is above the horizontal asymptote and to the left of the vertical asymptote, approaching both. The second branch is below the horizontal asymptote and to the right of the vertical asymptote, approaching both. A. Horizontal: y=4 Vertical: x=−3 Your answer is correct. B. Horizontal: none Vertical: x=−3 C. Horizontal: y=4 Vertical: none D. Horizontal: y=−3 Vertical: x=
A. Horizontal: y=4 Vertical: x=−3
Give a rule for the piecewise-defined function. Then give the domain and range. A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A graph has two branches. The first branch is a horizontal ray that extends to the left from an open circle at (2, negative 3). The second branch is a horizontal ray that extends to the right from a solid circle at (2, 3). A. f(x)=−3 if x<23 if x≥2 Domain: (−∞,∞) Range: {−3,3} B. f(x)=−3 if x≤23 if x>2 Domain: {−3,3} Range: (−∞,∞) C. f(x)=−3 if x<23 if x≥2 Domain: {−3,3} Range: (−∞,∞) D. f(x)=−3 if x≤23 if x>2 Domain: (−∞,∞) Range: {−3,3}
A. f(x)=−3 if x<23 if x≥2 Domain: (−∞,∞) Range: {−3,3}
Give the domain and range of the relation. {A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A V-shaped graph that opens downward has vertex (negative 5, 4) and passes through the points (negative 6, 3) and (negative 4, 3).} A. The domain is (−∞,∞). The range is (−∞,4]. B. The domain is (−∞,∞). The range is (−∞,4). C. The domain is (−∞,−5]. The range is (−∞,4]. D. The domain is (−∞,∞). The range is (−∞,∞).
A. The domain is (−∞,∞). The range is (−∞,4].
{NOT EDITED} Determine whether the following statement is true or false. If false, explain why. Because 2+5i is a zero of f(x)=x2−4x+29, we can conclude that 2−5i is also a zero. Is the statement true or false? A. The statement is true. B. The statement is false. Because 2+5i is a zero of f(x)=x2−4x+29, we can conclude that −5+2i is a zero, not 2−5i. C. The statement is false. Because 2+5i is a zero of f(x)=x2−4x+29, we can conclude that −2+5i is a zero, not 2−5i. D. The statement is false. Because 2+5i is a zero of f(x)=x2−4x+29, we can conclude that −2−5i is a zero, not 2−5i.
A. The statement is true.
Graph the function. f(x)=−4|x| Answer: In the shape of an upside-down V right on the y-axis (negative).
Answer: In the shape of an upside down V right on the y-axis (negative).
Q.52 Sketch the graph of the polynomial function. g(x)=(x−2)3(x+2) Choose the correct graph below. A. -1010-150150xy A coordinate plane has a horizontal x-axis from negative 10 to 10 in increments of 2 and a vertical y-axis from negative 150 to 150 in increments of 25. A smooth curve rises steeply in quadrant three to a maximum at (negative 2, 0), falls to a minimum in quadrant two comma rises and crosses the x axis at 30, rises and crosses the x-axis at (2, 0), and rises steeply in quadrant one. B. A coordinate plane has a horizontal x-axis from negative 10 to 10 in increments of 2 and a vertical y-axis from negative 150 to 150 in increments of 25. A smooth curve falls steeply in quadrant two and crosses the x-axis at negative 2 to a minimum in quadrant three comma falls and crosses the x axis at negative 15, rises and crosses the y-axis at 2, and rises steeply in quadrant 1. Your answer is correct. C. -1010-150150xy A coordinate plane has a horizontal x-axis from negative 10 to 10 in increments of 2 and a vertical y-axis from negative 150 to 150 in increments of 25. A smooth curve rises steeply crossing the x-axis at negative 2, rises to a maximum in quadrant two comma falls and crosses the x axis at 15, falls and crosses the x-axis at 2, and falls steeply in quadrant four. D. -1010-150150xy
B. A coordinate plane has a horizontal x-axis from negative 10 to 10 in increments of 2 and a vertical y-axis from negative 150 to 150 in increments of 25. A smooth curve falls steeply in quadrant two and crosses the x-axis at negative 2 to a minimum in quadrant three comma falls and crosses the x axis at negative 15, rises and crosses the y-axis at 2, and rises steeply in quadrant 1.
Decide whether the following statement is true or false. If false, tell why. For f(x)=(x+3)3(x−5), 3 is a zero of multiplicity 3. Choose the correct answer below. A. The statement is true. B. The statement is false because 3 is not a zero of f(x). C. The statement is false because 3 is a zero of multiplicity nothing.
B. The statement is false because 3 is not a zero of f(x).
Use the equation and the corresponding graph for the quadratic function to find the domain and range. f(x)=−2(x−3)^2+4 A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A parabola that opens downward has vertex (3, 4) and passes through the points (2, 2) and (4, 2). A. Domain: (−∞,∞); Range: [4,∞) B. Domain: (−∞,∞); Range: (−∞,4] C. Domain: (−∞,∞); Range: (−∞,∞) D. Domain: (−∞,4]; Range: (−∞,∞)
B. Domain: (−∞,∞); Range: (−∞,4]
Solve and graph the inequality. Give answer in interval notation. −9<−3x≤3 A. [−3,1) B. [-1,3) C. (-3,1) D. [-1,3]
B. [-1,3)
Solve the quadratic inequality. Write the solution set in interval notation. x^2−6x≤−8 A. [−4,−2] B. [2,4] C. (−4,−2) D. (−∞,−4]∪[−2,∞)
B. [2,4]
Simplify the power of i. i−23 A. −1 B. i C. 1 D. -i
B. i
Solve the equation. |5x−7/10|=8 A. {73/3,−29} B. {87/5,−73/5} C. {87/5} D. {5, -1/3}
B. {87/5, -73/5}
Solve the equation using the quadratic formula. 2x^2=−10x−6 A. −5± squ. root 134 B. −5± squ. root 132 C. −5± squ. root 372 D. −10± squ. root 132
B. −5± squ. root 132
Use the equation and the corresponding graph for the quadratic function to find the x-intercepts. f(x)=−2(x−8)^2+2 A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A parabola that opens downward has vertex (8, 2) and passes through the points (6, negative 6) and (10, negative 6). A. (−8,0) and (8,0) B. (0,7) and (0,9) C. (7,0) and (9,0) D. (6,0) and (10,0)
C. (7,0) and (9,0)
The graph of y=f(x) is given. Use the graph to find f(8). {A coordinate system has a horizontal x-axis labeled from negative 20 to 20 and a vertical y-axis labeled from negative 20 to 20. Each have 10 equally spaced tick marks. From left to right, a curve starts at a plotted point 5 tick marks to the left of and 3 tick marks above the origin, rises to a maximum, falls passing through a plotted point on the x-axis 3 tick marks to the left of the origin to a point in quadrant 3, rises to a plotted point on the y-axis 3 tick marks below the origin, falls to a minimum at a plotted point 2 tick marks to the right of and 4 tick marks below the origin, rises passing through a plotted point 3 tick marks to the right of and 2 tick marks below the origin and a plotted point 4 tick marks to the right of and 2 tick marks above the origin to a maximum in quadrant 1 and then falls to a plotted point on the x-axis 5 tick marks to the right of the origin. −20 −20 20xy 20} A. 0 B. 12 C. −16 D. 8
C. -16
Graph the equation. y=15x−4 A. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A line falls from left to right and passes through the points (0, negative 4) and (5, negative 5). B. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A line falls from left to right and passes through the points (0, 4) and (5, 3). C. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A line rises from left to right and passes through the points (0, 4) and (5, 5). D. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A line rises from left to right and passes through the points (0, 4) and (5, 5).
D. A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A line rises from left to right and passes through the points (0, 4) and (5, 5).
Graph the function. f(x)=|5x| A. -614-1010xy A coordinate system has a horizontal x-axis labeled from negative 6 to 14 in increments of 2 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A V-shaped graph that opens upward has vertex (5, 0) and passes through the points (4, 1) and (6, 1). B. -1010-55xy A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 2 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph that opens upward has vertex (0, 0) and passes through the points (negative 5, 1) and (5, 1). C. -55-1010xy A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 2. A V-shaped graph that opens downward has vertex (0, 0) and passes through the points (negative 1, negative 5) and (1, negative 5). D. In the shape of a V right on the y-axis.
D. In the shape of a V right on the y-axis (positive).
The comprehensive graph of a polynomial function y=f(x) is shown. How many real zeros does the function f have? A coordinate plane has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 150 to 150 in increments of 25. A function rises at an increasing rate from right to left at its left end and falls at an increasing rate from left to right at its right end. From left to right, the function crosses the horizontal axis from above at left parenthesis negative 5 comma 0 right parenthesis comma from below at left parenthesis negative 2 comma 0 right parenthesis and from above at left parenthesis 6 comma 0 right parenthesis. The function has a local minimum at approximately left parenthesis negative 3.6 comma negative 20 right parenthesis and a local maximum at approximately left parenthesis 2.9 comma 120 right parenthesis. The function intersects the vertical axis at approximately (0, 60). The function f has three real zero(s).
The function f has three real zero(s).
Factor f(x)=3x^3− 4x^2−35x+12 into linear factors given that −3 is a zero of f(x). f(x)=3x^3− 4x^2−35x+12= (x−4)(3x−1)(x+3)
(x−4)(3x−1)(x+3)
Solve the inequality. Write the solution set in interval notation. |x−2|> 3 A. (5,∞) B. (−1,5) C. (−∞,−1)∪(5,∞) D. undefined
C. (−∞,−1)∪(5,∞)
Which of these graphs is the graph of y=x? What is its domain? Graph A A coordinate system titled Graph A has a horizontal x-axis labeled from negative 4 to 4 in increments of 1 and a vertical y-axis labeled from negative 4 to 4 in increments of 1. From left to right, a curve rises at a decreasing rate passing through the point (negative 1, negative 1), is horizontal when passing through the point (0, 0), and rises at an increasing rate, passing through the point (1, 1). Graph B A coordinate system titled Graph B has a horizontal x-axis labeled from negative 1 to 5 in increments of 1 and a vertical y-axis labeled from negative 3 to 3 in increments of 1. A U-shaped curve that opens to the right has vertex (0, 0) and passes through (1, 1) and (1, negative 1). Graph C A coordinate system titled Graph C has a horizontal x-axis labeled from negative 4 to 4 in increments of 1 and a vertical y-axis labeled from negative 4 to 4 in increments of 1. A graph consists of 8 horizontal line segments, each extending from a solid circle on the left to an open circle on the right. Their endpoints are listed from left to right as follows: (negative 4, negative 4) and (negative 3, negative 4); (negative 3, negative 3) and (negative 2, negative 3); (negative 2, negative 2) and (negative 1, negative 2); (negative 1, negative 1) and (0, negative 1); (0, 0) and (1, 0); (1, 1) and (2, 1); (2, 2) and (3, 2); (3, 3) and (4, 3). A point is plotted at (4, 4). Graph D A coordinate system titled Graph D has a horizontal x-axis labeled from negative 2 to 6 in increments of 1 and a vertical y-axis labeled from negative 1 to 3 in increments of 0.5. A curve that rises from left to right at a decreasing rate starts at the point (0, 0) and passes through the points (1, 1) and (4, 2). graph D; [0,∞) graph B; [0,∞) graph C; {...,−4,−3,−2,−1,0,1,2,3,4,...} graph A; (−∞,∞)
graph D; [0,∞)
Determine if the function is even, odd, or neither. f(x)=−9x^3−5x^2+8 Odd Even Neither
Neither
Does the relation shown below define a function? {(−5,1),(−3,−6),(3,−5),(3,7)} Yes No
No
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first. 4x^4+10x^3−36x^2+73x+15;x+5 Is x+5 a factor of 4x^4+10x^3−36x^2+73x+15? No Yes
Yes
The function f(x)=−x^5+74x^3−108x^2−433x−252 has the graph given to the right. Use the graph to factor the polynomial. What is the factored form of the polynomial? f(x)=−(x+9)(x+1)^2(x−4)(x−7) (Simplify your answer. Type your answer in factored form. Factor completely.)
f(x)=−(x+9)(x+1)^2(x−4)(x−7)
The function defined by f(x)=x^4+7x^3−49x^2−343x has the graph as shown. Use the graph to factor the polynomial. A coordinate plane has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 1700 to 1700 in increments of 100. From left to right, a curve falls in quadrant 2 at a decreasing rate, touching the x-axis from above at (negative 7, 0) and turning back upwards, rises to a maximum then falls, crossing the x-axis at the origin to a minimum in quadrant 4, then rises again at an increasing rate, crossing the x-axis at (7, 0). What is the factored form of the polynomial? f(x)=x left parenthesis x plus 7 right parenthesis squared left parenthesis x minus 7 right parenthesis f(x)=(x+7)2(x−7) (Simplify your answer. Type your answer in factored form.)
f(x)=(x+7)2(x−7)
