Question 1

Evaluate the indicated function for   and   . ​   ​

Accepted Answer

A) 12 
B) -10 
C) 7 
D) 14 
E) 10 
A) 12 
B) -10 
C) 7 
D) 14 
E) 10

Question 2

Sketch the graph of the equation y = 4|x - 3| + 2. ​

Accepted Answer

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

Question 3

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|
​

Accepted Answer

A) f​-1(x) = x - 5 ​
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) f​-1(x) = x + 5 ​
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) f​-1(x) = x - 5 ​
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. 
D) f​-1(x) = x + 5 ​
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. 
E) f​-1(x) = x - 5 ​
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) f​-1(x) = x - 5 ​
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) f​-1(x) = x + 5 ​
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) f​-1(x) = x - 5 ​
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. 
D) f​-1(x) = x + 5 ​
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. 
E) f​-1(x) = x - 5 ​
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 4

​Find the x- and y-intercepts of the graph of the equation   . ​

Accepted Answer

A) ​x-intercept:   y-intercept: none 
B) ​x-intercept:   y-intercept:   
C) ​x-intercept:   y-intercept: none 
D) ​x-intercept:   y-intercept:   
E) ​​x-intercept:   y-intercept: none 
A) ​x-intercept:   y-intercept: none 
B) ​x-intercept:   y-intercept:   
C) ​x-intercept:   y-intercept: none 
D) ​x-intercept:   y-intercept:   
E) ​​x-intercept:   y-intercept: none

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

Evaluate the indicated function for   and   . ( fg )(1)

Accepted Answer

A) 15 
B) -35 
C) -23 
D) -25 
E) -33 
A) 15 
B) -35 
C) -23 
D) -25 
E) -33

Question 7

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4)p

Accepted Answer

A) associative property of addition 
B) commutative property of addition 
C) associative property of multiplication 
D) commutative property of multiplication 
E) distributive property 
A) associative property of addition 
B) commutative property of addition 
C) associative property of multiplication 
D) commutative property of multiplication 
E) distributive property

Question 8

Select the correct graph of the given function. ​   ​

Accepted Answer

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

Question 9

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 10

Write the following exponential expression in simplest form. ​   ​

Accepted Answer

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

Question 11

Graph the given function. f(x) = (x - 3)2

Accepted Answer

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

Question 12

Show algebraically that f and g are inverse functions.
f(x) = 9x + 9

Accepted Answer

The answer of Show algebraically that f and g are...

Question 13

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

Accepted Answer

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

Question 14

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 15

Rewrite the expression with positive exponents and simplify.   ​

Accepted Answer

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

Question 16

Determine whether the lines are parallel, perpendicular, or neither. ​
L1: y =   x - 9
L2: y = -   x - 2
​

Accepted Answer

A) Perpendicular 
B) Neither 
C) Parallel 
A) Perpendicular 
B) Neither 
C) Parallel

Question 17

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

Accepted Answer

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

Question 18

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function.
​   ​
Please give the answer as a simplified expression (not an equation).

Accepted Answer

The answer of Let f (x) = 2x + 1,...

Question 19

Select the correct graph of the given function. ​   ​

Accepted Answer

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

Question 20

Write an equation for the function that is described by the given characteristic. ​
The shape of   , but shifted three units to the left and reflected in both the x-axis and the y-axis.
​

Accepted Answer

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

Evaluate the indicated function for and .

Sketch the graph of the equation y = 4|x - 3| + 2.

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|

Find the x- and y-intercepts of the graph of the equation .

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

Evaluate the indicated function for and . ( fg )(1)

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4)p

Select the correct graph of the given function.

Use a graphing utility to graph the function.

Write the following exponential expression in simplest form.

Graph the given function. f(x) = (x - 3)²

Show algebraically that f and g are inverse functions. f(x) = 9x + 9

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

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

Rewrite the expression with positive exponents and simplify.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = x - 9 L2: y = - x - 2

Find and the domain of the composite function.

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. Please give the answer as a simplified expression (not an equation).

Select the correct graph of the given function.

Write an equation for the function that is described by the given characteristic. The shape of , but shifted three units to the left and reflected in both the x-axis and the y-axis.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Exam 7: Prerequisites

Evaluate the indicated function for and . ​ ​

Sketch the graph of the equation y = 4|x - 3| + 2. ​

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| ​

​Find the x- and y-intercepts of the graph of the equation . ​

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

Evaluate the indicated function for and . ( fg )(1)

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4)p

Select the correct graph of the given function. ​ ​

Use a graphing utility to graph the function. ​ ​

Write the following exponential expression in simplest form. ​ ​

Graph the given function. f(x) = (x - 3)2

Show algebraically that f and g are inverse functions. f(x) = 9x + 9

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

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

Rewrite the expression with positive exponents and simplify. ​

Determine whether the lines are parallel, perpendicular, or neither. ​ L1: y = x - 9 L2: y = - x - 2 ​

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

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. ​ ​ Please give the answer as a simplified expression (not an equation).

Select the correct graph of the given function. ​ ​

Write an equation for the function that is described by the given characteristic. ​ The shape of , but shifted three units to the left and reflected in both the x-axis and the y-axis. ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Evaluate the indicated function for and .

Sketch the graph of the equation y = 4|x - 3| + 2.

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|

Find the x- and y-intercepts of the graph of the equation .

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

Select the correct graph of the given function.

Use a graphing utility to graph the function.

Write the following exponential expression in simplest form.

Graph the given function. f(x) = (x - 3)²

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

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

Rewrite the expression with positive exponents and simplify.

Determine whether the lines are parallel, perpendicular, or neither. L1: y = x - 9 L2: y = - x - 2

Find and the domain of the composite function.

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. Please give the answer as a simplified expression (not an equation).

Select the correct graph of the given function.

Write an equation for the function that is described by the given characteristic. The shape of , but shifted three units to the left and reflected in both the x-axis and the y-axis.