Question 1

Find the graph of the equation. ​   ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​

Question 2

Solve the following equation. ​   ​

Accepted Answer

A)    
B) ​   
C) ​   
D) ​   
E) ​   
A)    
B) ​   
C) ​   
D) ​   
E) ​

Question 3

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. ​   ​

Accepted Answer

A) ​increasing on (-∞, ∞) 
B) descreasing on (-∞, 1) increasing on (1, ∞) 
C) ​increasing on (-∞, 1) descreasing on (1, ∞) 
D) ​descreasing on (-∞, ∞) 
E) descreasing on (1, 1) increasing on (1, ∞) 
A) ​increasing on (-∞, ∞) 
B) descreasing on (-∞, 1) increasing on (1, ∞) 
C) ​increasing on (-∞, 1) descreasing on (1, ∞) 
D) ​descreasing on (-∞, ∞) 
E) descreasing on (1, 1) increasing on (1, ∞)

Question 4

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​
F(x) = |x - 9| + 1
​

Accepted Answer

A) f-1(x) = x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
B) f-1(x) = x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
C) f-1(x) = -x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ -9. 
D) f-1(x) = x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ -9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
E) f-1(x) = -x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ 9. 
A) f-1(x) = x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
B) f-1(x) = x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
C) f-1(x) = -x - 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ -9. 
D) f-1(x) = x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ -9.The domain of f-1 and the range of f are all real numbers x such that x ≥ 1. 
E) f-1(x) = -x + 8 The domain of f and the range of f-1 are all real numbers x such that x ≥ 1.The domain of f-1 and the range of f are all real numbers x such that x ≥ 9.

Question 5

Determine whether the function has an inverse function.If it does, find the inverse function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) No Inverse 
A)    
B)    
C)    
D)    
E) No Inverse

Question 6

Select the correct graph of the given function. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 7

Find (f + g)(x). ​   ​

Accepted Answer

A) 2x 
B) 4x 
C) -4x 
D) -2x 
E) 2x + 8 
A) 2x 
B) 4x 
C) -4x 
D) -2x 
E) 2x + 8

Question 8

Find the zeroes of the functions algebraically. ​   ​

Accepted Answer

A)    
B)    
C) ​   
D)    
E)    
A)    
B)    
C) ​   
D)    
E)

Question 9

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is ​
​   ​
X-intercept:   y-intercept:   ​
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Use the graph of   to write an equation for the function whose graph is shown. ​
​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Evaluate the function   at   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​   ​

Accepted Answer

A)    
B) ​   
C) ​   
D) ​   
E) None of the above 
A)    
B) ​   
C) ​   
D) ​   
E) None of the above

Question 13

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. ​   ​

Accepted Answer

A)    m = -3
Y-intercept: (0,2) 
B)    m is undefined.There is no y-intercept. 
C)    ​m = -2
Y-intercept: (0,3) 
D)    ​ m is undefined.There is no y-intercept. 
E) ​   m is undefined.There is no y-intercept. 
A)    m = -3
Y-intercept: (0,2) 
B)    m is undefined.There is no y-intercept. 
C)    ​m = -2
Y-intercept: (0,3) 
D)    ​ m is undefined.There is no y-intercept. 
E) ​   m is undefined.There is no y-intercept.

Question 14

Write an equation for the function that is described by the given characteristic. ​
The shape of   , but shifted 17 units to the right.
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find all solutions of the following equation in the interval [0, 2π). ​   ​

Accepted Answer

A)    
B) No solution 
C) ​   
D) ​   
E) ​   
A)    
B) No solution 
C) ​   
D) ​   
E) ​

Question 16

The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by   , where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of   .Round to the nearest foot.

Accepted Answer

A) 260 
B) 346 
C) 173 
D) 303 
E) 87 
A) 260 
B) 346 
C) 173 
D) 303 
E) 87

Question 17

Select the graph of f and f-1 on the same set of coordinate axes. ​   ​

Accepted Answer

A)    ​ 
B)    
C) ​   
D) ​   
E)    
A)    ​ 
B)    
C) ​   
D) ​   
E)

Question 18

Rationalize the denominator of the following expression and then simplify your answer. ​   ​

Accepted Answer

A)    
B)    
C)    
D)      
E)    
A)    
B)    
C)    
D)      
E)

Question 19

Evaluate the function at the specified value of the independent variable and simplify.   f(y - 5)​

Accepted Answer

A) ​ f(y - 5)=   ​ 
B) ​ f(y - 5)=   ​ 
C) ​ f(y - 5)=   ​ 
D) ​ f(y - 5)=   ​ 
E) f(y - 5)=   ​
​ 
A) ​ f(y - 5)=   ​ 
B) ​ f(y - 5)=   ​ 
C) ​ f(y - 5)=   ​ 
D) ​ f(y - 5)=   ​ 
E) f(y - 5)=   ​
​

Question 20

Which equation does not represent y as a function of x? ​

Accepted Answer

A) ​2x = 8y 
B) -4y = -8 
C) ​5x2 + 5y = 3 
D) ​3x + 6y = -5 
E) ​7y2 + 8x = 9 
A) ​2x = 8y 
B) -4y = -8 
C) ​5x2 + 5y = 3 
D) ​3x + 6y = -5 
E) ​7y2 + 8x = 9

Find the graph of the equation.

Solve the following equation.

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x) = |x - 9| + 1

Determine whether the function has an inverse function.If it does, find the inverse function.

Select the correct graph of the given function.

Find (f + g)(x).

Find the zeroes of the functions algebraically.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is X-intercept: y-intercept:

Use the graph of to write an equation for the function whose graph is shown.

Evaluate the function at .

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd.

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line.

Write an equation for the function that is described by the given characteristic. The shape of , but shifted 17 units to the right.

Find all solutions of the following equation in the interval [0, 2π).

Select the graph of f and f^-1 on the same set of coordinate axes.

Rationalize the denominator of the following expression and then simplify your answer.

Evaluate the function at the specified value of the independent variable and simplify. f(y - 5)

Which equation does not represent y as a function of x?

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

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Exam 7: Prerequisites

Find the graph of the equation. ​ ​

Solve the following equation. ​ ​

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. ​ ​

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f-1.State the domains and ranges of f and f-1. ​ F(x) = |x - 9| + 1 ​

Determine whether the function has an inverse function.If it does, find the inverse function. ​ ​

Select the correct graph of the given function. ​ ​

Find (f + g)(x). ​ ​

Find the zeroes of the functions algebraically. ​ ​

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is ​ ​ ​ X-intercept: y-intercept: ​ ​

Use the graph of to write an equation for the function whose graph is shown. ​ ​ ​

Evaluate the function at . ​

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​ ​

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. ​ ​

Write an equation for the function that is described by the given characteristic. ​ The shape of , but shifted 17 units to the right. ​

Find all solutions of the following equation in the interval [0, 2π). ​ ​

Select the graph of f and f-1 on the same set of coordinate axes. ​ ​

Rationalize the denominator of the following expression and then simplify your answer. ​ ​

Evaluate the function at the specified value of the independent variable and simplify. f(y - 5)​

Which equation does not represent y as a function of x? ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Find the graph of the equation.

Solve the following equation.

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. F(x) = |x - 9| + 1

Determine whether the function has an inverse function.If it does, find the inverse function.

Select the correct graph of the given function.

Find (f + g)(x).

Find the zeroes of the functions algebraically.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is X-intercept: y-intercept:

Use the graph of to write an equation for the function whose graph is shown.

Evaluate the function at .

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd.

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line.

Write an equation for the function that is described by the given characteristic. The shape of , but shifted 17 units to the right.

Find all solutions of the following equation in the interval [0, 2π).

Select the graph of f and f^-1 on the same set of coordinate axes.

Rationalize the denominator of the following expression and then simplify your answer.

Evaluate the function at the specified value of the independent variable and simplify. f(y - 5)

Which equation does not represent y as a function of x?