Question 1

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=-|x|$

Accepted Answer

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

Question 2

Find the x-intercept(s)and the y-intercept of the function.
-f(x)= -2

Accepted Answer

A) (-2, 0), no y-intercept 
B) no x-intercept, (0, -2) 
C) no x-intercept, no y-intercept 
D) (-2, 0), (0, -2) 
A) (-2, 0), no y-intercept 
B) no x-intercept, (0, -2) 
C) no x-intercept, no y-intercept 
D) (-2, 0), (0, -2)

Question 3

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = | x - 3 | + 2$$

Accepted Answer

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

Question 4

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-(- 1, 0)

Accepted Answer

A) constant 
B) decreasing 
C) increasing 
A) constant 
B) decreasing 
C) increasing

Question 5

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
-$f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , \frac { 1 } { 6 } \right) \cup \left( \frac { 1 } { 6 } , \infty \right)$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 4 x + 5 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left( \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 5 } { 4 } , \infty \right)$

Question 6

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) function 
B) not a function 
A) function 
B) not a function

Question 7

Find the domain of the composite function f g. Write the domain in interval notation.
-$$f ( x ) = 8 x + 56 , g ( x ) = x + 6$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 7 , - 6 ) ( - 6 , \infty )$ 
C)  $( - \infty , - 13 ) \cup ( - 13 , \infty )$ 
D)  $( - \infty , 13 ) \cup ( 13 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 7 , - 6 ) ( - 6 , \infty )$ 
C)  $( - \infty , - 13 ) \cup ( - 13 , \infty )$ 
D)  $( - \infty , 13 ) \cup ( 13 , \infty )$

Question 8

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 9

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

Accepted Answer

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

Question 10

Find the rule that defines each piecewise-defined function.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0  0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x \geq 0 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } x > 0 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0  0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x \geq 0 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } x > 0 \end{array} \right.$

Question 11

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) function 
B) not a function 
A) function 
B) not a function

Question 12

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Accepted Answer

A) f has a relative maximum at x = 0; the relative maximum is 1 
B) f has a relative maximum at x = -3 and 3; the relative maximum is 0 
C) f has no relative maximum 
D) f has a relative maximum at x = 3; the relative maximum is 1 
A) f has a relative maximum at x = 0; the relative maximum is 1 
B) f has a relative maximum at x = -3 and 3; the relative maximum is 0 
C) f has no relative maximum 
D) f has a relative maximum at x = 3; the relative maximum is 1

Question 13

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
-

Accepted Answer

A)  domain: $[ 0,4 ]$
range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$
range: $[ 0,4 ]$ 
C)  domain: $( - \infty , \infty )$
range: $[ 3,4 ]$ 
D)  domain: $[ 3,4 ]$
range: $( - \infty , \infty )$ 
A)  domain: $[ 0,4 ]$
range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$
range: $[ 0,4 ]$ 
C)  domain: $( - \infty , \infty )$
range: $[ 3,4 ]$ 
D)  domain: $[ 3,4 ]$
range: $( - \infty , \infty )$

Question 14

For the given functions f and g, find the requested composite function.
-$f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$.

Accepted Answer

A)  $8 \sqrt { x + 7 } - 11$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x + 1 }$ 
A)  $8 \sqrt { x + 7 } - 11$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x + 1 }$

Question 15

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=\sqrt{x-3}-6$

Accepted Answer

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

Question 16

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 17

Solve the problem.
-A cellular phone plan had the following schedule of charges:  
 What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Accepted Answer

$27.50 $32.50; \[C ( x ) = \left\{ \begi

Question 18

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { x + 3 }$$

Accepted Answer

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

Question 19

The graph of a function f is given. Use the graph to answer the question.
-Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Accepted Answer

A) f has a relative minimum at x = 0; the relative minimum is 2 
B) f has no relative minimum 
C) f has a relative minimum at x = -2 and 2; the relative minimum is 0 
D) f has a relative minimum at x = -2; the relative minimum is 0 
A) f has a relative minimum at x = 0; the relative minimum is 2 
B) f has no relative minimum 
C) f has a relative minimum at x = -2 and 2; the relative minimum is 0 
D) f has a relative minimum at x = -2; the relative minimum is 0

Question 20

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.
-$y=2 f(x)$

Accepted Answer

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

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-|x|$

Find the x-intercept(s)and the y-intercept of the function. -f(x)= -2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Use the vertical line test to determine whether the graph represents a function. -

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

Use the horizontal line test to determine whether the function is one-to-one. -

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

Find the rule that defines each piecewise-defined function. -

Use the vertical line test to determine whether the graph represents a function. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 3: Functions

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=−∣x∣f(x)=-|x|f(x)=−∣x∣

Find the x-intercept(s)and the y-intercept of the function. -f(x)= -2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=∣x−3∣+2f ( x ) = | x - 3 | + 2f(x)=∣x−3∣+2

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 1, 0)

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - f(x)=4x+5;g(x)=6x−1;f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quadf(x)=4x+5;g(x)=6x−1; Find fg\frac { f } { g }gf​

Use the vertical line test to determine whether the graph represents a function. -

Find the domain of the composite function f g. Write the domain in interval notation. - f(x)=8x+56,g(x)=x+6f ( x ) = 8 x + 56 , g ( x ) = x + 6f(x)=8x+56,g(x)=x+6

Use the horizontal line test to determine whether the function is one-to-one. -

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

Find the rule that defines each piecewise-defined function. -

Use the vertical line test to determine whether the graph represents a function. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

For the given functions f and g, find the requested composite function. - f(x)=x+7,g(x)=8x−11;f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quadf(x)=x+7​,g(x)=8x−11; Find the function f∘gf \circ gf∘g .

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x−3−6f(x)=\sqrt{x-3}-6f(x)=x−3​−6

Decide whether or not the functions are inverses of each other. - f(x)=x+3,x≥−3;g(x)=x2+3f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3f(x)=x+3​,x≥−3;g(x)=x2+3

Solve the problem. -A cellular phone plan had the following schedule of charges: What is the charge for 200 minutes of calls in one month? What is the charge for 250 minutes of calls in one month? Construct a function that relates the monthly charge C for x minutes of calls.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=1x+3f ( x ) = \frac { 1 } { x + 3 }f(x)=x+31​

The graph of a function f is given. Use the graph to answer the question. -Find the values of x, if any, at which f has a relative minimum. What are the relative minima?

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y=2f(x)y=2 f(x)y=2f(x)

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-|x|$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x - 3 | + 2$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation. - $f ( x ) = 4 x + 5 ; g ( x ) = 6 x - 1 ; \quad$ Find $\frac { f } { g }$

Find the domain of the composite function f g. Write the domain in interval notation. - $f ( x ) = 8 x + 56 , g ( x ) = x + 6$

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 7 } , g ( x ) = 8 x - 11 ; \quad$ Find the function $f \circ g$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y=2 f(x)$