Question 1

Decide whether the relation defines a function.
-$$y = x ^ { 2 }$$

Accepted Answer

A)  Not a function 
B)  Function 
A)  Not a function 
B)  Function

Question 2

Use the graph to solve the problem.
-During which hour did the temperature increase the most?

Accepted Answer

A)  12 p.m. to 1 p.m. 
B)  9 a.m. to 10 a.m. 
C)  1 p.m. to 2 p.m. 
D)  10 a.m. to 11 a.m. 
A)  12 p.m. to 1 p.m. 
B)  9 a.m. to 10 a.m. 
C)  1 p.m. to 2 p.m. 
D)  10 a.m. to 11 a.m.

Question 3

Match the description with the correct symbolic expression.
-a linear function whose graph has y-intercept -4

Accepted Answer

A)  $y = - 4 x + 16$ 
B)  $f ( x ) = - 5 x - 4$ 
C)  $- 4 x + 12 y = 16$ 
D)  $x = - 4$ 
A)  $y = - 4 x + 16$ 
B)  $f ( x ) = - 5 x - 4$ 
C)  $- 4 x + 12 y = 16$ 
D)  $x = - 4$

Question 4

Graph the function.
-$f(x)=|x|+5$

Accepted Answer

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

Question 5

Give a rule for the piecewise-defined function. Then give the domain and range.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} \right.$; Domain: $( - \infty , \infty )$, Range: $( - \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 2 & \text { if } x > 1 \end{array} \right.$; Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$, Range: $( - \infty , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x & \text { if } x \leq 1 \ 2 x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 2 ) \cup ( 2 , \infty )$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 1 & \text { if } x > 1 \end{array} \right.$; Domain: $( - \infty , \infty )$, Range: $( - \infty , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \ x + 2 & \text { if } x > 1 \end{array} \right.$; Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$, Range: $( - \infty , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x & \text { if } x \leq 1 \ 2 x + 1 & \text { if } x > 1 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 2 ) \cup ( 2 , \infty )$

Question 6

Graph the line described.
-$\text { through }(5,-2) ; m=0$

Accepted Answer

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

Question 7

Determine if the function is even, odd, or neither.
-$$f ( x ) = - 4 x ^ { 4 } - 5 x + 7$$

Accepted Answer

A)  Odd 
B)  Neither 
C)  Even 
A)  Odd 
B)  Neither 
C)  Even

Question 8

Solve the problem.
-Along with incomes, peopleʹs charitable contributions have steadily increased over the past few years. The table below shows the average deduction for charitable contributions reported on
Individual income tax returns over 6 years. Find the average rate of change per year between year
3 and year 5.

Accepted Answer

A)  $\$ 320$ per year 
B)  $\$ 610$ per year 
C)  $\$ 305$ per year 
D)  $\$ 355$ per year 
A)  $\$ 320$ per year 
B)  $\$ 610$ per year 
C)  $\$ 305$ per year 
D)  $\$ 355$ per year

Question 9

Give the domain and range of the relation.
-$$y = \frac { 17 } { 2 - x }$$

Accepted Answer

A)  domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; range: $( - \infty , \infty )$ 
A)  domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; range: $( - \infty , \infty )$

Question 10

Graph the function.
-$$g ( x ) = - \sqrt { x + 2 } - 1$$

Accepted Answer

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

Question 11

Find the specified domain.
-Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 3 x } { x - 6 }$ and $g ( x ) = \frac { 4 } { x + 1 }$

Accepted Answer

A)  $( - \infty , - 4 ) \cup ( - 4 , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 1 ) \cup ( - 1,6 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6,1 ) \cup ( 1 , \infty )$ 
A)  $( - \infty , - 4 ) \cup ( - 4 , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , - 1 ) \cup ( - 1,6 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6,1 ) \cup ( 1 , \infty )$

Question 12

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = \frac { x } { 7 - x }$$

Accepted Answer

A)  $\frac { h x } { ( 7 - x - h ) ( 7 + x ) }$ 
B)  $- \frac { 7 } { ( 7 - x + h ) ( 7 - x ) }$ 
C)  $\frac { x } { ( 7 - x + h ) ( 7 - x ) }$ 
D)  $\frac { 7 } { ( 7 - x - h ) ( 7 - x ) }$ 
A)  $\frac { h x } { ( 7 - x - h ) ( 7 + x ) }$ 
B)  $- \frac { 7 } { ( 7 - x + h ) ( 7 - x ) }$ 
C)  $\frac { x } { ( 7 - x + h ) ( 7 - x ) }$ 
D)  $\frac { 7 } { ( 7 - x - h ) ( 7 - x ) }$

Question 13

Give a rule for the piecewise-defined function. Then give the domain and range.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 3 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , 3 ] \cup [ 3 , \infty )$, Range: $( - \infty , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x < 3 \ 2 x + 3 & \text { if } x \geq 3 \end{array} ; \right.$ Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$, Range: $( - \infty , \infty )$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 3 ] \cup [ 3 , \infty )$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 2 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , \infty )$, Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \ - 3 & \text { if } x = 3 \end{array} ; \right.$ Domain: $( - \infty , 3 ] \cup [ 3 , \infty )$, Range: $( - \infty , \infty )$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x < 3 \ 2 x + 3 & \text { if } x \geq 3 \end{array} ; \right.$ Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$, Range: $( - \infty , \infty )$

Question 14

Graph the function.
-$f(x)=|6 x|$

Accepted Answer

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

Question 15

For the given functions f and g , find the indicated composition.
-$$f ( x ) = \frac { x - 10 } { 7 } , \quad g ( x ) = 7 x + 10$$
$( g \circ f ) ( x )$

Accepted Answer

A)  $x$ 
B)  $x - \frac { 10 } { 7 }$ 
C)  $x + 20$ 
D)  $7 x + 60$ 
A)  $x$ 
B)  $x - \frac { 10 } { 7 }$ 
C)  $x + 20$ 
D)  $7 x + 60$

Question 16

Find the center-radius form of the equation of the circle.
-center $( 0,0 )$, radius 7

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 7 }$ 
B)  $x ^ { 2 } + y ^ { 2 } = 14$ 
C)  $x ^ { 2 } + y ^ { 2 } = 49$ 
D)  $x ^ { 2 } + y ^ { 2 } = 7$ 
A)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 7 }$ 
B)  $x ^ { 2 } + y ^ { 2 } = 14$ 
C)  $x ^ { 2 } + y ^ { 2 } = 49$ 
D)  $x ^ { 2 } + y ^ { 2 } = 7$

Question 17

Refer to the following graphs to determine an appropriate response.  
-Which graphs of functions increase over the whole of their domain?

Accepted Answer

A)  graph D 
B)  graphs A and D 
C)  graphs $C$ and $D$ 
D)  graphs $A$ and $B$ 
A)  graph D 
B)  graphs A and D 
C)  graphs $C$ and $D$ 
D)  graphs $A$ and $B$

Question 18

Evaluate the function.
-Find $f ( - 4 )$ when $f ( x ) = x ^ { 2 } - 2 x + 3$

Accepted Answer

A)  11 
B)  27 
C)  5 
D)  21 
A)  11 
B)  27 
C)  5 
D)  21

Question 19

Find the slope and the y-intercept of the line.
-$$8 x + 7 y = 37$$

Accepted Answer

A)  slope: $\frac { 7 } { 8 } ; \mathrm { y }$-intercept: $\frac { 7 } { 37 }$ 
B)  slope: $- \frac { 8 } { 7 } ; y$-intercept: $\frac { 37 } { 7 }$ 
C)  slope: $\frac { 8 } { 7 } ; \mathrm { y } - \mathrm { intercept } : \frac { 37 } { 7 }$ 
D)  slope: $- \frac { 7 } { 8 } ; y$-intercept: $\frac { 7 } { 37 }$ 
A)  slope: $\frac { 7 } { 8 } ; \mathrm { y }$-intercept: $\frac { 7 } { 37 }$ 
B)  slope: $- \frac { 8 } { 7 } ; y$-intercept: $\frac { 37 } { 7 }$ 
C)  slope: $\frac { 8 } { 7 } ; \mathrm { y } - \mathrm { intercept } : \frac { 37 } { 7 }$ 
D)  slope: $- \frac { 7 } { 8 } ; y$-intercept: $\frac { 7 } { 37 }$

Question 20

The graph of y = f(x) is given. Use the graph to find the function value.
- 
Find $f ( - 3 )$.

Accepted Answer

A)  $- 3$ 
B)  None of these 
C)  $- 5$ 
D)  2 
A)  $- 3$ 
B)  None of these 
C)  $- 5$ 
D)  2

Decide whether the relation defines a function. - $y = x ^ { 2 }$

Use the graph to solve the problem. -During which hour did the temperature increase the most?

Match the description with the correct symbolic expression. -a linear function whose graph has y-intercept -4

Graph the function. - $f(x)=|x|+5$

Give a rule for the piecewise-defined function. Then give the domain and range. -

Graph the line described. - $\text { through }(5,-2) ; m=0$ $Graph the line described. - \text { through }(5,-2) ; m=0$

Determine if the function is even, odd, or neither. - $f ( x ) = - 4 x ^ { 4 } - 5 x + 7$

Give the domain and range of the relation. - $y = \frac { 17 } { 2 - x }$

Graph the function. - $g ( x ) = - \sqrt { x + 2 } - 1$ $Graph the function. - g ( x ) = - \sqrt { x + 2 } - 1$

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 3 x } { x - 6 }$ and $g ( x ) = \frac { 4 } { x + 1 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x } { 7 - x }$

Give a rule for the piecewise-defined function. Then give the domain and range. -

Graph the function. - $f(x)=|6 x|$

For the given functions f and g , find the indicated composition. - $f ( x ) = \frac { x - 10 } { 7 } , \quad g ( x ) = 7 x + 10$ $( g \circ f ) ( x )$

Find the center-radius form of the equation of the circle. -center $( 0,0 )$ , radius 7

Refer to the following graphs to determine an appropriate response. -Which graphs of functions increase over the whole of their domain?

Evaluate the function. -Find $f ( - 4 )$ when $f ( x ) = x ^ { 2 } - 2 x + 3$

Find the slope and the y-intercept of the line. - $8 x + 7 y = 37$

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( - 3 )$ .

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Decide whether the relation defines a function. - y=x2y = x ^ { 2 }y=x2

Use the graph to solve the problem. -During which hour did the temperature increase the most?

Match the description with the correct symbolic expression. -a linear function whose graph has y-intercept -4

Graph the function. - f(x)=∣x∣+5f(x)=|x|+5f(x)=∣x∣+5

Give a rule for the piecewise-defined function. Then give the domain and range. -

Graph the line described. - through (5,−2);m=0\text { through }(5,-2) ; m=0 through (5,−2);m=0

Determine if the function is even, odd, or neither. - f(x)=−4x4−5x+7f ( x ) = - 4 x ^ { 4 } - 5 x + 7f(x)=−4x4−5x+7

Give the domain and range of the relation. - y=172−xy = \frac { 17 } { 2 - x }y=2−x17​

Graph the function. - g(x)=−x+2−1g ( x ) = - \sqrt { x + 2 } - 1g(x)=−x+2​−1

Find the specified domain. -Find the domain of (f−g)(x)( f - g ) ( x )(f−g)(x) when f(x)=3xx−6f ( x ) = \frac { 3 x } { x - 6 }f(x)=x−63x​ and g(x)=4x+1g ( x ) = \frac { 4 } { x + 1 }g(x)=x+14​

Compute and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 - f(x)=x7−xf ( x ) = \frac { x } { 7 - x }f(x)=7−xx​

Give a rule for the piecewise-defined function. Then give the domain and range. -

Graph the function. - f(x)=∣6x∣f(x)=|6 x|f(x)=∣6x∣

For the given functions f and g , find the indicated composition. - f(x)=x−107,g(x)=7x+10f ( x ) = \frac { x - 10 } { 7 } , \quad g ( x ) = 7 x + 10f(x)=7x−10​,g(x)=7x+10 (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Find the center-radius form of the equation of the circle. -center (0,0)( 0,0 )(0,0) , radius 7

Refer to the following graphs to determine an appropriate response. -Which graphs of functions increase over the whole of their domain?

Evaluate the function. -Find f(−4)f ( - 4 )f(−4) when f(x)=x2−2x+3f ( x ) = x ^ { 2 } - 2 x + 3f(x)=x2−2x+3

Find the slope and the y-intercept of the line. - 8x+7y=378 x + 7 y = 378x+7y=37

The graph of y = f(x) is given. Use the graph to find the function value. - Find f(−3)f ( - 3 )f(−3) .

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Decide whether the relation defines a function. - $y = x ^ { 2 }$

Graph the function. - $f(x)=|x|+5$

Graph the line described. - $\text { through }(5,-2) ; m=0$ $Graph the line described. - \text { through }(5,-2) ; m=0$

Determine if the function is even, odd, or neither. - $f ( x ) = - 4 x ^ { 4 } - 5 x + 7$

Give the domain and range of the relation. - $y = \frac { 17 } { 2 - x }$

Graph the function. - $g ( x ) = - \sqrt { x + 2 } - 1$ $Graph the function. - g ( x ) = - \sqrt { x + 2 } - 1$

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 3 x } { x - 6 }$ and $g ( x ) = \frac { 4 } { x + 1 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x } { 7 - x }$

Graph the function. - $f(x)=|6 x|$

For the given functions f and g , find the indicated composition. - $f ( x ) = \frac { x - 10 } { 7 } , \quad g ( x ) = 7 x + 10$ $( g \circ f ) ( x )$

Find the center-radius form of the equation of the circle. -center $( 0,0 )$ , radius 7

Evaluate the function. -Find $f ( - 4 )$ when $f ( x ) = x ^ { 2 } - 2 x + 3$

Find the slope and the y-intercept of the line. - $8 x + 7 y = 37$

The graph of y = f(x) is given. Use the graph to find the function value. - Find $f ( - 3 )$ .