Advanced Algebra midterm

State how many complex and real zeros the function has. f(x) = x3 - 16x2 + 79x - 120

3 complex zeros; all 3 real

Solve the equation. x2- 6x + 34 = 0

3+-5i

Solve the problem. In the following formula, y is the minimum number of hours of studying required to attain a test score of x: y=0.52x/(100.5-x) How many hours of study are needed to score 88?

3.66hr

A rock falls from a tower that is 132.3 m high. As it is falling, its height is given by the formula h = 132.3 - 4.9t2. How many seconds will it take for the rock to hit the ground (h=0)?

5.2 s

Write the product in standard form. (6 + 4i)( 7 - 3i)

54+10i

Find the remainder when f(x) is divided by (x - k) f(x) = 2x2 + 3x2 + 4x + 18 k = - 2

6

Write the number in scientific notation. 0.0000088316

8.8316 x 10^-6

Solve the inequality algebraically. Write the solution in interval notation. |x+3| <= 6

[-9,3]

Find the range of the function. f(x)=rad(8+x)

[0,infinity)

Solve the equation using the quadratic formula. 7x2+8x = -2

x=(-4+rad2)/7 or x=(-4-rad2)/7

Solve the equation by factoring. 6x2 - 29x - 5 = 0

x=-1/6 or x=5

Find the axis of the graph of the function. f(x) = (x + 2)2 - 9

x=-2

((7x+7)/5)+((6x-2)/2)=-1

x=-7/22

Solve the equation. (x+7)/8 = (x+8)/9

x=1

Find the asymptotes of the given function. h(x)= ((x-1)(x+5))/(x^2-4) vertical asymptotes

x=2, x=-2

Solve the equation graphically by finding x-intercepts. x3 - 6x2 + 12x - 10 = 0

x=3.26

Use a method of your choice to solve the equation. |2x-9|=4

x=5/2 or x=13/2

Solve the equation 3/(x-4) = 1+5/(x+4)

x=6 or -8

Find an equation for the circle. Center (0, -6), radius 11

x^2+(y+6)^2=121

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. Through (5, -3), perpendicular to -7x - 3y = -44

y=(3/7x)-(36/7)

Solve the equation. (y - 11) - (y + 10) = 4y

y=-21/4

Given k = 5 is a zero of f(x) = 5x3 + 6x2 + 2x + 4 , determine if k is an upper-bound.

yes

Write the statement using absolute value notation. The distance between y and -8 is greater than 3.

|y+8|>3

Perform the requested operation or operations. Find the domain of each. f(x)=6x+8; g(x)=3x^2 find (fg)(x)

18x^3+34x^2; domain(-infinity, infinity)

Find all rational zeros. f(x) = x3 - 3x2 - 4x + 12

2,3,-2

Write the sum or difference in the standard form a + bi. ( 8 + 4i) - ( -9 + i)

17+3i

Solve the polynomial inequality. x4 - 104x2 + 400 < 0

( -10, -2) ∪ ( 2, 10)

Find the vertex of the graph of the function. f(x) = 4x2 + 32x + 63

(-4,-1)

Solve the inequality. (3x+4)/(7x^2+7)>0

(-4/3,∞)

Find the domain of the given function f(x)=x/(x-3)

(-infinity, 3) U (3, infinity)

Solve the polynomial inequality. (x + 10)(x + 1)(x - 3) < 0

(-∞, -10) ∪ ( -1, 3)

Find the midpoint of the line segment with the given endpoints. (2, -9) and (-1, 6)

(1/2, -3/2)

Solve the inequality. 9/(x-4) > 7/(x-4)

(4,∞)

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. f(x) = x3 + 4x2 - 5x - 20

-4(rational), rad5 (irrational), and -rad5 (irrational)

Find the zeros of the function. f(x) = x3 + 12x2 + 47x + 60

-5,-3,and -4

Find the slope of the line through the pair of points. (6, -2) and (4, -2)

0

Find the zeros of the function. f(x) = x3- 49x

0,7,-7

Write the number in decimal form. 3.971 × 10-5

0.00003971

Write the expression in standard form. i/(2+i)

1/5 +2/5i

Use an equation to solve the problem. One positive number is twice another positive number. The sum of the two numbers is 360. Find the two numbers.

120,240

Identify intervals on which the function is increasing, decreasing, or constant. g(x) =0.5(x+6)^2

Increasing: (-6, infinity); Decreasing: (-infinity, -6)

Determine if the function is a power function. If it is, then state the power and constant of variation. f(x)=-1/7x^2

Power is 2; constant of variation is -1/7

Describe how to transform the graph of f into the graph of g. f(x)= radx and g(x)=-rad(x+6)

Shift the graph of f left 6 units and then reflect across the x-axis.

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.

exponential regression

Perform the requested operation or operations. f(x) = 7x + 14; g(x) = 4x - 1 Find f(g(x)).

f(g(x))=28x+7

Perform the requested operation or operations. f(x)=rad(x+7); g(x)=8x-11

f(g(x))=2rad(2x-1)

Divide f(x) by d(x), and write a summary statement in the form indicated. f(x) = x2 - 2x + 3 d(x) = x - 4 Write answers in polynomial form

f(x)=(x-4)(x+2)+11

Choose the one alternative that best completes the statement or answers the question. Write an equation for the linear function f satisfying the given conditions. f(-1) = -5 and f(5) = 7

f(x)=2x-3

Find functions f and g so that h(x)=f(g(x)) y=|8x+3|

f(x)=|x|, g(x)=8x+3

Find the inverse of the function f(x)=6/(x+3)

f^-1(x)=6/x -3

Find the inverse of the function. f(x)=x^3+7

f^-1(x)=^3rad(x-7)

Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = 8x4 + 5x + 4

neither

Determine whether the power function is even, odd, or neither. f(x)=8x^(8/10)

neither

Write the statement as a power function equation. Use k as the constant of variation. John kept track of the time it took him to drive to college from his home and the speed at which he drove. He found that the time t varies inversely as the speed r.

t=k/r

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. y = 2x - x3

unbounded