AB Calc Review Questions

Use your calculator to solve the given inequality x^2-3x-7<0

(-1.541, 4.541)

Given the equation, what is the x-interval when y > 0? y = 9 - x^2

(-3,3)

Given the equation, what is/are the x-interval(s) when y≤0 for y=4-x^2

(-∞, -2] U [2, +∞)

restrict the domain √(x+3/x-5)

(-∞, -3] U (5, +∞)

Rewrite the following absolute value as a piecewise function: g(x)=|x+5|−3

g(x)={x+2, if x≥−5, −x−8, ifx<−5}

Select the domain and range of the function, y=√(x−3) +4

y≥ 4 x≥ 3

(2x-5/x-2) ≤ 1

(2,3]

factor the polynomial completely 2x^3+x^2-18x-9

(2x+1)(x+3)(x-3)

Simplify the following expressions 2/ x+1 + 3/x-2

(5x-1)/(x+1)(x-2)

Solve for x, ln(2x+3)=5

(e^5 -3)/2

3e^4x =8

(ln8-ln3)/ 4

(x^2 +24)/ (x^2 -4) + -7/(x-2)/(x-5)/ x^2 +9x+14

(x+7)

Select the equation of the circle that has endpoints of (6, 4) and (-2, -2) for a diameter of the circle.

(x-2)^2 + (y-1)^2 = 25

Changing into standard form by completing the square: x^2 + y^2 - 8x + 2y +8 = 0

(x-4)^2 + (y+1)^2 = 9

find an equation for the circle whose diameter has endpoints (3,-4) and (6,0).

(x-4.5)^2 +(y+2)^2 = (5/2)^2

Which of the following is a valid restricted domain of the equation, y = 2 sin x - 1, that would produce a one-to-one graph? (π/4,3π/4) (π/2,3π/2) [0,π] [π,7π/4]

(π/2,3π/2)

Solve: 2/x+1<3/x−2

(−7,−1)∪(2,+∞)

Solve: 7≤2−5x<9

(−7/5,−1]

Solve: 3+7x≤2x−9

(−∞,−12/5]

Solve. x^2−3x>10

(−∞,−2)∪(5,+∞)

Restrict the domain so that the results are only in the set of real numbers. √x^2−4 non-negative: x≥0

(−∞,−2]∪[2,+∞)

Solve: x^2≥25

(−∞,−5]∪[5,+∞)

log 0.51

-.292

ln 0.91

-0.094

find the slope: (2,9) and (4,3)

-3

Evaluate -27^2/3

-9

find the slope: (-2,7) and (5,7)

0

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). cosθ=1

0+2π, where N { E

5e^3x =9

0.196

Solve for x, 6e^2x=11 Round your answer to three decimal places.

0.303

7^√0.9

0.985

Determine if the following examples represent discrete data or continuous data: 1. The number of coins in a stack of coins. [ Select ] ["Discrete", "Continuous"] 2. The distance from the earth to the moon. [ Select ] ["Continuous", "Discrete"] 3. The amount of applesauce left in a jar. [ Select ] ["Continuous", "Discrete"] 4. The number of apples in a bag. [ Select ] ["Continuous", "Discrete"] 5. The time left in a 60 minutes run. [ Select ] ["Continuous", "Discrete"] 6. The number of eggs in a carton. [ Select ] ["Continuous", "Discrete"] 7. The number of pearls on a necklace. [ Select ] ["Discrete", "Continuous"]

1. discrete 2. continuous 3. continuous 4. discrete 5. continuous 6. discrete 7. discrete

Name the domain, range, and zeros of each function y=x y=x^2 y=x^3 y=1/x y= √x y= 3^√x

1. domain= reals, range= reals, zeros= (0,0) 2. domain= reals, range= [0, +∞), zeros: (0,0) 3. domain=reals, range= reals, zeros: (0,0) 4. domain= reals, x≠0, range=reals, y≠0, zeros: none 5. domain= x≥0, range= [0, +∞), zeros: (0,0) 6. domain= reals, range=reals, zeros:(0,0)

Given y= 5 - √x What is the x-value when y= 6 What is the x-value when y= 0 What is the x-interval(s) when y≥ 2 What is the maximum y-value of the graph?

1. no solution 2. x=25 3. 0≤x≤9 4.(0,5)

Write the expanded expression log (4^√x+3 / sin3x)

1/4log(x+3)-log(sin(3x))

log x^7/2 + log √x^3 =15

1000

Select all of the values that are a valid solution to the equation. (Select ALL that apply.) (√x)^2=16 16 -4 4 -16

16

f(x)= 3x+4 g(x)= x^2 find f(g(-2))

16

if lim x-->2 f(x)= -5 find lim x--->-5 f^-1(x) =

2

log3 11

2.183

log2 5

2.322

log2 7=

2.807

Write the expanded expression ln(b^2 / 3ac^3)

2lnb - ln3 - lna -3lnc

find and simplify (f(w)-f(x))/ w-x

2w + 2x

ln e^2x

2x

find and simplify (f(x+h)-f(x))/ h

2x + h

Find the value for θ in radians that satisfies the given equation over the interval 0≤θ≤2π, (Select ALL that apply.) Cscθ=Undefined 2π π 0 3π/2

2π, π, and 0

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). tanθ=-√3

2π/3 + πN, where N { E

Solve for x √x^2 = 3

3 or -3

Solve the polynomial equation using synthetic division and the quadratic formula 2x^3-7x^2-16x+35=0

3+√2 and 3-√2

f(x)=3x+4 g(x)= x^2 find g(f(5))

361

Expand the expression completely, ln (x^3√x-8)/ 3sin2x

3lnx+1/2ln(x−8)−ln3−lnsin(2x)

log3 81=

4

Simplify the following expressions (2x-6)/(3x^2-18x) / (x^2-x-6)/ (6x-36)

4/ x(x+2)

Given f(x)=3x−7f(x)=3x−7 and g(x)=4x2g(x)=4x2, calculate g(f(−1)).

400

Simplify the expression 5/x+2 - 1/x-3

4x-17 / (x+2)(x-3)

ln e^5

5

Simplify the expression (10/ x^2-9) + (5/x+3) / x-1 / (X^2 + 5x +6)

5(x+2) / (x-3)

2^2.37

5.169

Given f(x)=5x−4 g(x)=3x2 calculate f(g(−2))

56

Select all of the values that are a valid solution to the equation: (Select ALL that apply.) √x^2=6 -36 -6 6 36

6 and -6

If limx→7 g(x)=−3 , find limx→−3 g^−1(x)=

7

solve for x xe^x -7e^x =0

7

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). sinθ= -1/2

7π/6 11π/6 ----------- 7π/6 +2πN 11π/6 + 2πN, where N { E

(-27)^2/3

9

Which characteristics describe a required property of a function? The graph is a smooth curve. A vertical line that is passing through the graph will only pass through a single point on the graph. This is correct. If any vertical line touches the graph just one time, it means the corresponding independent variable is used just one time. All of the y-value are unique, where y is the dependent variable. All of the x-values are unique, where x is the independent variable.

A vertical line that is passing through the graph will only pass through a single point on the graph. All of the x-values are unique, where x is the independent variable.

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). secθ=undefined

π/2 + πN, where N {E

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). sinθ=0

πN, where N {E

An open box is to be made from a 14-inch by 32-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the squares to be cut from the corners to create a box with a maximum volume. Let V(x) be the function of the volume of the box that results when the squares have sides of the length x. Find a formula for V(x) as a function of x. Find the domain of x What is the measure of x when the volume is a maximum?

V(x)=(14-2x)(32-2x)(x) domain of x: 0<x<7 Measure of x when the volume is a maximum: (3.036, 624.072)

Separate each function into tis composite functions h(x)= sin^3x

f(x)=x^3 g(x)= sinx

Separate each function into tis composite functions h(x)= √4-3x

f(x)=√x g(x)= (4-3x)

Which of the following is a valid restricted domain of the equation, y = 3 cos x + 5, that would produce a one-to-one graph? (3π/4,3π/2) [0,π][0,π] (π/2,3/π2) (−π/4,π/4)

[0,π]

Solve. 9x^3−12x^2−11x−2≥0

[−1/3]∪[2,+∞)

find the domain and range of: (a.) f(x)= 2 + √x-1 (b.) f(x)= (x+1)(x-1)

a. Domain: [1, +∞) Range: [2, +∞) b. Domain: x≠1 ; (-∞, 1) U (1, +∞) Range: y≠1 ; (-∞, 1) U (1, +∞)

find the natural domain of: (a.) f(x)= x^3 (b.)= f(x)= 1/(x-1)(x-3) (c.)= f(x)= tanx (d.)= f(x)= √x^2-5x+6

a. Reals b. (-∞, 1) U (1,3) U (3,+∞) c. +- ℼ/2; N}E d. (-∞, 2] U [3, +∞)

An open box is to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. (a.) Let V be the volume of the box that results when the squares have sides of length x. (b.) Find the Domain of V

a. V(x)= (16-2x)(30-2x)(x) = 480x-92x^2+4x^3 b. Domain: 0≤x≤8

Draw a rough sketch of the graph to determine whether the function is one-to-one a. f(x)= √x+3 b. f(x)= |x-2|

a. one-to-one : d: [-3, +∞) b. not one-to-one : ND (-∞, +∞) one-to-one : D: (-∞, 2] and D: [2, +∞)

find the inverse of each function f(x)= √3x-1

f^-1(x)= (x^2 +1)/ 3 D: x≥0

Find the inverse of the function, f(x)=√2x+5

f^-1(x)= (x^2 - 5)/2

find the inverse of each function f(x)= 2x+7

f^-1(x)= x-7/2

Graph the parabola, list the axis of symmetry and vertex: y= x^2 + 2x -8

ax. of sym. = -1 v(-1, 9)

Graph the parabola, list the axis of symmetry and vertex: y=x^2 - 2x - 2

ax. of sym. = 1 v(1,-3)

Graph the parabola, list the axis of symmetry and vertex: y= -x^2 + 4x - 5

ax. of sym. = 2 v(2, -1)

Show that f and g are inverses of each other f(x)= 2x+3 g(x)= x-3/2

both equal x

Given the equation of the circle, find the center and radius (x+4)^2 + y^2 = 5

c(-4,0) r=√5

Identify the center of the following circle as an ordered pair: What is the radius of the circle? x^2 + y^2 - 4x -6y - 3 = 0

c(2,3) r=4

Given the equation of the circle, find the center and radius (x-2)^2 + (y-5)^2 = 9

c(2,5) r=3

Find the distance between A and B, where a=-2 and b=10

d=12

solve for x ln (x-2) =8

e^8 +2

The points (4 2k) and (6, -1) lie on a line with a slope of m=1/3. Find the new value for k.

k=-5/6

The points (5, -2) and (14, k) lie on a line with a slope of m=23m=23. Find the value of k.

k=4

Rewrite as a single logarithm 3ln(x+2) + 1/2lnx - ln(sinx)

ln(x+2)^3 + lnx / ln(sinx)

3^-x =7

ln7/-ln3

Expand the expression completely, log3(4x^5sinx)/√x^2+7

log3(4)+5log3x+log3sinx−1/2log3(x^2+7)

Determine if the equation is one-to-one, y=(x−1)^2

not one-to-one

Determine if the equation is one-to-one, f(x)=x^3−4

one-to-one

Separate each function into tis composite functions h(x)= cos(x+1)^2

r(x)= cosx s(x)= x^2 t(x)= x=1

Separate each function into tis composite functions h(x)= cos^2 (x+1)

r(x)= x^2 s(x)= cosx t(x)= (x+1)

Graph y=4 - |x-2|

reflect across the x-axis v(2,4)

Graph y= 3^√2-x

reflect across the y-axis v(2,0)

The value of an angle 0 is given. Find the values of all six trigonometric functions of 0 without using a calculator. 1. 135 degrees 2. -2pi/3

see Appendix 4

Find the slope and y-intercept. y=3x+7

slope= 3 y-int.= 7

Separate h(x) into its composite functions where h(x) = t(s(r(x))) for h(x)= √x-5 +4

t(x)= x+4 s(x)= x-5 r(x)=√x

Separate h(x) into its composite functions where h(x) = t(s(r(x))) for h(x)=sin^3(x+7)

t(x)= x^3 s(x)= sinx r(x)= x+7

Separate h(x) into its composite functions where h(x) = t(s(r(x))) for h(x)=cosx−−√x +5 A. x + 5 B. √x C. cos x

t. A. s. C. r. B.

Select all of the characteristics of the graph of the given equation. y= √4-(x-3)^2 Radius is 4 Top-half of a circle Right-half of a circle Center at (3, -4) Center at (3, 0) Radius of 2

top-half of a circle center at (3,0) Radius of 2

TRUE or FALSE If A and B are points on a coordinate line that have the coordinates "a" and "b" respectively, then the distance between those points may be represented as d=|a−b|d=|a−b| or d=|b−a|d=|b−a|.

true

Graph the parabola: x= -y^2 + 4y -5

v(-1,2)

Find and graph the equation of the left half of the parabola for: y= 9 - x^2

v(0,9) x= -√9-y

Describe the vertex of the parabola as an ordered pair: Write the equation for the axis of symmetry (i.e. x = 4 or y = -1): y= x^2 - 2x + 3

v(1,2) x=1

Find the vertex of the parabola by completing the square. Write the vertex as an ordered pair. y^2−6y+2x−13=0

v(11,3)

Graph y=x^2 -4x +5

v(2,1) y=(x-2)^2 + 1

Graph the equation: y= -√x-3

v(3,0) x=(y-0)^2 + 3

Select all of the characteristics of the graph of the equation, y= -√x-4 Bottom-half of a parabola Left-half of a parabola Vertex at (4, 0) Vertex at (-4, 0)

v(4,0) bottom-half of parabola

10^logx

x

log 10^x

x

Simplify the following expressions: (5/x^2 -4) + 1/(x+2) / (3/x+2) + (2/x-2)

x+3/ 5x-2

e^ln(x-2)

x-2

Select all the characteristics of the graph of the equation, x= y^2 + 6y + 5 x - intercept at (5, 0) Vertex at (-4, -3) y - intercept at (0, -5) y - intercept at (0, 5) x - intercept at (1, 0) y - intercept at (0, -1)

x-int. at (5,0) v(-4,-3) y-int. (0,-5) y-int. (0,-1)

Write the equation for the left semi-circle from the following equation: x^2 + y^2 -4x - 6y - 3 = 0

x= 2- √16-(y-3)^2

log7 7^x =-3

x=-3

Select all of the asymptotes for the given function, y=(2x^2−2x−8)/3x^2+6x

x=0 x=-2 y=2/3

log16 2=x

x=1/4

log x^5/2 -log√x =4

x=100

If f(x)= 3x^2 -5x +12 find x if f^-1(x)=2

x=14

Solve for x ; 3xe^x -9e^x =0

x=3

log3 27=x

x=3

xe^x -3e^x =0

x=3

Solve for x (√x)^2 =5

x=5

lne (x+1) =5

x=e^5 -1

e^2x -3e^x =10

x=ln5

Graph the real solution set for the equation y=-√16-x^2

x^2 + y^2 = 16 c(0,0) r= 4

ln e^x^2-2

x^2 - 2

A particle begins at the position of (-2, -4) on a coordinate plane and moves along a line with a slope of 3 to a new position at x = 4. Write an equation in point - slope form and determine the new value for y.

y + 4 = 3(x + 2); when x = 4, y = 14

Write the equation of the line with the given characteristics. m=1 (2, -5)

y+5=1(x-2)

Write the equation of the line with the given characteristics. (3,4) and (2, -5)

y-4=9(x-3)

Find the equation of the top function that makes up the graph for: x= -y^2 + 4y - 5

y= 2 + √-x-1

A particle begins at the point (-1,2) and moves along a line with a slope of -3 to a new position where x=3. Find the new y-value.

y=-10

Graph and Solve: y^2 -2y-x=0

y=0 y=2

Find the equation of the top and bottom functions that make up the graph for: x= -y^2 +4y -5

y=2+-√-x-1

Find the equation for the bottom half of the circle: x^2 + y^2 +4x - 6y + 9 = 0

y=3-√4-(x+2)^2

Rewrite the equation as a piece-wise function without an absolute value symbol: y=2+|x-3|

y={-x+5 if x < 3 x-1 if x ≥ 3}

Find all values of Theta (in radians) that satisfy the given equation. (Do not use a calculator). tanθ=0

πN, where N {E

e^lnℼ

ℼ