Question 1

Graph the function.
-f(x)= x2

Accepted Answer

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

Question 2

The function f is one-to-one. State the domain and the range of f and fS1U1P1-1S1S1P0. Write the domain and range in set-builder
notation.
-$$f ( x ) = \frac { 1 } { 4 x + 3 }$$

Accepted Answer

A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq - 3 \}$;
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 3 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 3 } { 4 } \right\} \right.$$ 
B)  $f ( x ) : D = \left\{ x \mid x z - \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq 0 \}$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y \neq - \frac { 3 } { 4 } \right\}$$ 
C)  $f ( x )$ : D is all real numbers, $R$ is all real numbers;
 $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $\mathrm { R }$ is all real numbers 
D)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 1 } { 4 } \right\} , R = \left\{ y \mid y \neq \frac { 1 } { 3 } \right\}$
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 3 } \right\} , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 1 } { 4 } \right\}$$ 
A)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq - 3 \}$;
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } | \mathrm { x } \neq - 3 \rangle , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 3 } { 4 } \right\} \right.$$ 
B)  $f ( x ) : D = \left\{ x \mid x z - \frac { 3 } { 4 } \right\} , R = \{ y \mid y \neq 0 \}$;
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 0 \} , R = \left\{ y \mid y \neq - \frac { 3 } { 4 } \right\}$$ 
C)  $f ( x )$ : D is all real numbers, $R$ is all real numbers;
 $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $\mathrm { R }$ is all real numbers 
D)  $f ( x ) : D = \left\{ x \mid x \neq \frac { 1 } { 4 } \right\} , R = \left\{ y \mid y \neq \frac { 1 } { 3 } \right\}$
$$\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 3 } \right\} , R = \left\{ \mathrm { y } \mid \mathrm { y } \neq \frac { 1 } { 4 } \right\}$$

Question 3

For the given functions f and g, find the requested composite function.
-$f ( x ) = \frac { x - 3 } { 8 } , g ( x ) = 8 x + 3 ; \quad$ Find the function $g$ of

Accepted Answer

A)  $8 x + 21$ 
B)  $x$ 
C)  $x - \frac { 3 } { 8 }$ 
D)  $x + 6$ 
A)  $8 x + 21$ 
B)  $x$ 
C)  $x - \frac { 3 } { 8 }$ 
D)  $x + 6$

Question 4

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

Accepted Answer

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

Question 5

Find the x-intercept(s)and the y-intercept of the function.
-$$F ( x ) = 2 x ^ { 2 } - 10 x - 12$$

Accepted Answer

A)  $( - 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$ 
B)  $( - 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$ 
C)  $( 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$ 
D)  $( 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$ 
A)  $( - 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$ 
B)  $( - 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$ 
C)  $( 6,0 ) , ( 1,0 ) , ( 0 , - 12 )$ 
D)  $( 6,0 ) , ( - 1,0 ) , ( 0 , - 12 )$

Question 6

The graph of a function f is given. Use the graph to answer the question.
-What are the x-intercepts?

Accepted Answer

A)  $( - 12,0 )$ 
B)  $( - 12,0 ) , ( 14,0 )$ 
C)  $( - 12,0 ) , ( 14,0 ) , ( 20,0 )$ 
D)  $( - 20,0 ) , ( - 12,0 ) , ( 14,0 ) , ( 20,0 )$ 
A)  $( - 12,0 )$ 
B)  $( - 12,0 ) , ( 14,0 )$ 
C)  $( - 12,0 ) , ( 14,0 ) , ( 20,0 )$ 
D)  $( - 20,0 ) , ( - 12,0 ) , ( 14,0 ) , ( 20,0 )$

Question 7

Determine whether the function is one-to-one.
-f(x)= 7

Accepted Answer

A) One-to-one 
B) Not one-to-one 
A) One-to-one 
B) Not one-to-one

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 by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = 7 | x |$$

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

The graph of a function f is given. Use the graph to answer the question.
-Use the graph of f given below to find f(-12).

Accepted Answer

A) 20 
B) -8 
C) 0 
D) -12 
A) 20 
B) -8 
C) 0 
D) -12

Question 12

Evaluate the function at the indicated value.
-Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = x ^ { 2 } + 7 x + 4$

Accepted Answer

A)  1 
B)  $2 x + h + 4$ 
C)  $2 x + h + 7$ 
D)  $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 8 } { h }$ 
A)  1 
B)  $2 x + h + 4$ 
C)  $2 x + h + 7$ 
D)  $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 8 } { h }$

Question 13

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=\sqrt{x}+5$

Accepted Answer

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

Question 14

Determine whether the equation defines y as a function of x.
-$$- 7 x + x ^ { 2 } - 48 = y$$

Accepted Answer

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

Question 15

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.
-$$y = - \frac { 1 } { 2 } f ( x )$$

Accepted Answer

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

Question 16

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 17

Evaluate.
-Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 4 x - 7$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 4$.

Accepted Answer

A)  $- \frac { 19 } { 7 }$ 
B)  1 
C)  $\frac { 5 } { 7 }$ 
D)  0 
A)  $- \frac { 19 } { 7 }$ 
B)  1 
C)  $\frac { 5 } { 7 }$ 
D)  0

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.
-$f(x)=\frac{1}{4} \sqrt{x}$

Accepted Answer

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

Question 19

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { x + 3 } + 2$$

Accepted Answer

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

Question 20

Find the intersection of the given intervals.
-$( 7 , \infty ) \cap [ 19 , \infty )$

Accepted Answer

A)  $( 7,19 ]$ 
B)  $( 7 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 19 , \infty )$ 
A)  $( 7,19 ]$ 
B)  $( 7 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 19 , \infty )$

Graph the function. -f(x)= x2

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder notation. - $f ( x ) = \frac { 1 } { 4 x + 3 }$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { x - 3 } { 8 } , g ( x ) = 8 x + 3 ; \quad$ Find the function $g$ of

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

Find the x-intercept(s)and the y-intercept of the function. - $F ( x ) = 2 x ^ { 2 } - 10 x - 12$

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

Determine whether the function is one-to-one. -f(x)= 7

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

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = 7 | x |$

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(-12).

Evaluate the function at the indicated value. -Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = x ^ { 2 } + 7 x + 4$

Determine whether the equation defines y as a function of x. - $- 7 x + x ^ { 2 } - 48 = y$

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y = - \frac { 1 } { 2 } f ( x )$ $Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y = - \frac { 1 } { 2 } f ( x )$

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

Evaluate. -Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 4 x - 7$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 4$ .

Find the intersection of the given intervals. - $( 7 , \infty ) \cap [ 19 , \infty )$

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. -f(x)= x2

The function f is one-to-one. State the domain and the range of f and f-1. Write the domain and range in set-builder notation. - f(x)=14x+3f ( x ) = \frac { 1 } { 4 x + 3 }f(x)=4x+31​

For the given functions f and g, find the requested composite function. - f(x)=x−38,g(x)=8x+3;f ( x ) = \frac { x - 3 } { 8 } , g ( x ) = 8 x + 3 ; \quadf(x)=8x−3​,g(x)=8x+3; Find the function ggg of

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

Find the x-intercept(s)and the y-intercept of the function. - F(x)=2x2−10x−12F ( x ) = 2 x ^ { 2 } - 10 x - 12F(x)=2x2−10x−12

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

Determine whether the function is one-to-one. -f(x)= 7

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

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)=7∣x∣f ( x ) = 7 | x |f(x)=7∣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)=1x−1f ( x ) = \frac { 1 } { x } - 1f(x)=x1​−1

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(-12).

Evaluate the function at the indicated value. -Find f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ when f(x)=x2+7x+4f ( x ) = x ^ { 2 } + 7 x + 4f(x)=x2+7x+4

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+5f(x)=\sqrt{x}+5f(x)=x​+5

Determine whether the equation defines y as a function of x. - −7x+x2−48=y- 7 x + x ^ { 2 } - 48 = y−7x+x2−48=y

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y=−12f(x)y = - \frac { 1 } { 2 } f ( x )y=−21​f(x)

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

Evaluate. -Find (fg)(−3)\left( \frac { f } { g } \right) ( - 3 )(gf​)(−3) when f(x)=4x−7f ( x ) = 4 x - 7f(x)=4x−7 and g(x)=5x2+14x+4g ( x ) = 5 x ^ { 2 } + 14 x + 4g(x)=5x2+14x+4 .

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)=14xf(x)=\frac{1}{4} \sqrt{x}f(x)=41​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)=1x+3+2f ( x ) = \frac { 1 } { x + 3 } + 2f(x)=x+31​+2

Find the intersection of the given intervals. - (7,∞)∩[19,∞)( 7 , \infty ) \cap [ 19 , \infty )(7,∞)∩[19,∞)

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

The function f is one-to-one. State the domain and the range of f and f^-1. Write the domain and range in set-builder notation. - $f ( x ) = \frac { 1 } { 4 x + 3 }$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { x - 3 } { 8 } , g ( x ) = 8 x + 3 ; \quad$ Find the function $g$ of

Find the x-intercept(s)and the y-intercept of the function. - $F ( x ) = 2 x ^ { 2 } - 10 x - 12$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = 7 | x |$

Evaluate the function at the indicated value. -Find $\frac { f ( x + h ) - f ( x ) } { h }$ when $f ( x ) = x ^ { 2 } + 7 x + 4$

Determine whether the equation defines y as a function of x. - $- 7 x + x ^ { 2 } - 48 = y$

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - $y = - \frac { 1 } { 2 } f ( x )$ $Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation. - y = - \frac { 1 } { 2 } f ( x )$

Evaluate. -Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 4 x - 7$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 4$ .

Find the intersection of the given intervals. - $( 7 , \infty ) \cap [ 19 , \infty )$