Question 1

Graph the piecewise-defined function. ​   ​

Accepted Answer

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

Question 2

Select the linear function such that it has the indicated function values. ​   ​

Accepted Answer

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

Question 3

Simplify the following radical expression.   ​

Accepted Answer

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

Question 4

Find the inverse of the one-to-one function.
​
y = 5x + 4
​
f -1(x) = __________

Accepted Answer

Question 5

The graph of a function is sketched below. ​   ​
Determine the interval on which the function is decreasing.
​

Accepted Answer

A) (-∞, -3] ∩ [-1, ∞) 
B) ​[-3, -1] 
C) ​[-1, -1] ​ 
D) ​[1, 3] ​ 
E) (-∞, -3] ∩ [-1, ∞) ​ 
A) (-∞, -3] ∩ [-1, ∞) 
B) ​[-3, -1] 
C) ​[-1, -1] ​ 
D) ​[1, 3] ​ 
E) (-∞, -3] ∩ [-1, ∞) ​

Question 6

Find all real values of x such that f(x) = 0. ​   ​

Accepted Answer

A) x = ±12 
B) x = ±13 
C) x = ±11 
D) x = ±10 
E) x = ±9 
A) x = ±12 
B) x = ±13 
C) x = ±11 
D) x = ±10 
E) x = ±9

Question 7

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 - 5)2
​

Accepted Answer

A)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
B)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ -5. 
C)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
D)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ 5. 
E)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ -5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
A)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
B)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ -5. 
C)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0. 
D)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ 0.The domain of f-1 and the range of f are all real numbers x such that x ≥ 5. 
E)    ​
The domain of f and the range of f-1 are all real numbers x such that x ≥ -5.The domain of f-1 and the range of f are all real numbers x such that x ≥ 0.

Question 8

Sketch the subset on the real number line, and state whether the interval is bounded or unbounded. ​
(-2, 2]
​

Accepted Answer

A)    The interval is unbounded. 
B)    The interval is unbounded. 
C)    The interval is bounded. 
D)    The interval is bounded. 
E)    The interval is unbounded. 
A)    The interval is unbounded. 
B)    The interval is unbounded. 
C)    The interval is bounded. 
D)    The interval is bounded. 
E)    The interval is unbounded.

Question 9

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 10

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function ​   ​
And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function   , where t represents the year, with t = 0 corresponding to 2000.
Evaluate the function   for t = 0 and 3.

Accepted Answer

A) h(0) = 0.1060, h(3) = 0.0783 
B) h(0) = 0.3060, h(3) = 0.2783 
C) h(0) = -0.2060, h(3) = -0.1783 
D) h(0) = 0.1783, h(3) = 0.2060 
E) h(0) = -0.1060, h(3) = -0.0783 
A) h(0) = 0.1060, h(3) = 0.0783 
B) h(0) = 0.3060, h(3) = 0.2783 
C) h(0) = -0.2060, h(3) = -0.1783 
D) h(0) = 0.1783, h(3) = 0.2060 
E) h(0) = -0.1060, h(3) = -0.0783

Question 11

Find   .

Accepted Answer

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

Question 12

Find (f - g)(x). ​   ​

Accepted Answer

A) 2x - 6 
B) 6 
C) 2x - 3 
D) 2x + 6 
E) 2x 
A) 2x - 6 
B) 6 
C) 2x - 3 
D) 2x + 6 
E) 2x

Question 13

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. ​
Y = 2 - |x|
​

Accepted Answer

A) x- intercept: (±2, 0) y- intercept: (0, 2)
Y-axis symmetry
​   ​ 
B) x- intercept: (-2, 0) y- intercept: (0, 2)
Y-axis symmetry   
C) x- intercept: (2, 0) y- intercept: (0, ±2)
Y-axis symmetry   
D) x- intercept: (2, 0) y- intercept: (0, 2)
Y-axis symmetry   
E) x- intercept: (-2, 0) y- intercept: (0, 2)
Y-axis symmetry   
A) x- intercept: (±2, 0) y- intercept: (0, 2)
Y-axis symmetry
​   ​ 
B) x- intercept: (-2, 0) y- intercept: (0, 2)
Y-axis symmetry   
C) x- intercept: (2, 0) y- intercept: (0, ±2)
Y-axis symmetry   
D) x- intercept: (2, 0) y- intercept: (0, 2)
Y-axis symmetry   
E) x- intercept: (-2, 0) y- intercept: (0, 2)
Y-axis symmetry

Question 14

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​   ​
​

Accepted Answer

A)    The function has an inverse. 
B) ​   The function has an inverse. 
C) ​   The function has an inverse. 
D) ​   The function has an inverse. 
E) ​   The function has an inverse. 
A)    The function has an inverse. 
B) ​   The function has an inverse. 
C) ​   The function has an inverse. 
D) ​   The function has an inverse. 
E) ​   The function has an inverse.

Question 15

Identify the terms.Then identify the coefficients of the variable terms of the expression. ​
6x + 2
​

Accepted Answer

A) 6x and 2 are the terms; 6 is the coefficient. 
B) 6x and 2 are the terms; -2 is the coefficient. 
C) 6x and 2 are the terms; -6 is the coefficient. 
D) 6x and 2 are the terms; 2 is the coefficient. 
E) 6 and 2 are the terms; 6 is the coefficient. 
A) 6x and 2 are the terms; 6 is the coefficient. 
B) 6x and 2 are the terms; -2 is the coefficient. 
C) 6x and 2 are the terms; -6 is the coefficient. 
D) 6x and 2 are the terms; 2 is the coefficient. 
E) 6 and 2 are the terms; 6 is the coefficient.

Question 16

Sketch the graph of the equation   . ​

Accepted Answer

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

Question 17

​Find   and the domain of the composite function. ​   ​

Accepted Answer

A)    Domain of   : all real numbers x except   
B)    Domain of   : all real numbers x except   
C)    Domain of   : all real numbers x except   
D)    Domain of   : all real numbers x except   
E)    Domain of   : all real numbers x except   
A)    Domain of   : all real numbers x except   
B)    Domain of   : all real numbers x except   
C)    Domain of   : all real numbers x except   
D)    Domain of   : all real numbers x except   
E)    Domain of   : all real numbers x except

Question 18

Find all real values of x such that f(x) = 0. ​
F(x) = x2 - 8x - 20
​

Accepted Answer

A) x = -10, 2 
B) x = -10, -2 
C) x = 2, 10 
D) x = -2, 10 
E) x = -8, 8 
A) x = -10, 2 
B) x = -10, -2 
C) x = 2, 10 
D) x = -2, 10 
E) x = -8, 8

Question 19

Use the functions given by   and g(x) = x3 to find (g-1 º f-1)(-5). ​

Accepted Answer

A) -2 
B) 0 
C) -4 
D) 2 
E) 4 
A) -2 
B) 0 
C) -4 
D) 2 
E) 4

Question 20

Select the correct graph, showing f and g are inverse functions. ​   ​

Accepted Answer

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

Graph the piecewise-defined function.

Select the linear function such that it has the indicated function values.

Simplify the following radical expression.

Find the inverse of the one-to-one function. y = 5x + 4 f ^-1(x) = __________

The graph of a function is sketched below. Determine the interval on which the function is decreasing.

Find all real values of x such that f(x) = 0.

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 - 5)²

Sketch the subset on the real number line, and state whether the interval is bounded or unbounded. (-2, 2]

Use a graphing utility to graph the function.

Find .

Find (f - g)(x).

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = 2 - |x|

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.

Identify the terms.Then identify the coefficients of the variable terms of the expression. 6x + 2

Sketch the graph of the equation .

Find and the domain of the composite function.

Find all real values of x such that f(x) = 0. F(x) = x² - 8x - 20

Use the functions given by and g(x) = x³ to find (g^-1 _º f^-1)(-5).

Select the correct graph, showing f and g are inverse functions.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Exam 7: Prerequisites

Graph the piecewise-defined function. ​ ​

Select the linear function such that it has the indicated function values. ​ ​

Simplify the following radical expression. ​

Find the inverse of the one-to-one function. ​ y = 5x + 4 ​ f -1(x) = __________

The graph of a function is sketched below. ​ ​ Determine the interval on which the function is decreasing. ​

Find all real values of x such that f(x) = 0. ​ ​

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 - 5)2 ​

Sketch the subset on the real number line, and state whether the interval is bounded or unbounded. ​ (-2, 2] ​

Use a graphing utility to graph the function. ​ ​

Find .

Find (f - g)(x). ​ ​

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. ​ Y = 2 - |x| ​

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​ ​ ​

Identify the terms.Then identify the coefficients of the variable terms of the expression. ​ 6x + 2 ​

Sketch the graph of the equation . ​

​Find and the domain of the composite function. ​ ​

Find all real values of x such that f(x) = 0. ​ F(x) = x2 - 8x - 20 ​

Use the functions given by and g(x) = x3 to find (g-1 º f-1)(-5). ​

Select the correct graph, showing f and g are inverse functions. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Graph the piecewise-defined function.

Select the linear function such that it has the indicated function values.

Simplify the following radical expression.

Find the inverse of the one-to-one function. y = 5x + 4 f ^-1(x) = __________

The graph of a function is sketched below. Determine the interval on which the function is decreasing.

Find all real values of x such that f(x) = 0.

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 - 5)²

Sketch the subset on the real number line, and state whether the interval is bounded or unbounded. (-2, 2]

Use a graphing utility to graph the function.

Find (f - g)(x).

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = 2 - |x|

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.

Identify the terms.Then identify the coefficients of the variable terms of the expression. 6x + 2

Sketch the graph of the equation .

Find and the domain of the composite function.

Find all real values of x such that f(x) = 0. F(x) = x² - 8x - 20

Use the functions given by and g(x) = x³ to find (g^-1 _º f^-1)(-5).

Select the correct graph, showing f and g are inverse functions.