Question 1

Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$$f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }$$

Accepted Answer

A)  Yes, no 
B)  No, no 
C)  Yes, yes 
D)  No, yes 
A)  Yes, no 
B)  No, no 
C)  Yes, yes 
D)  No, yes

Question 2

Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = \frac { 2 } { x - 8 }$

Accepted Answer

A)  $\left( \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , 8 \right) \cup ( 8 , \infty )$ 
B)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
A)  $\left( \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , 8 \right) \cup ( 8 , \infty )$ 
B)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 3

The figure below shows the graph of a function y = f(x). Use this graph to
-$$\text { Sketch the graph of } y = - f ( x ) \text {. }$$

Accepted Answer

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

Question 4

Graph the line and give the domain and the range.
-$$3 y + 18 = 0$$

Accepted Answer

A)  $D = \{ - 6 \} , R = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , R = \{ - 6 \}$
  
C)  $D = \{ - 6 \} , \quad R = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 6 \}$
  
A)  $D = \{ - 6 \} , R = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , R = \{ - 6 \}$
  
C)  $D = \{ - 6 \} , \quad R = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 6 \}$

Question 5

Find the center-radius form of the circle described or graphed.
-Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$.

Accepted Answer

A)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
B)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
A)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
B)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$

Question 6

Find the average rate of change illustrated in the graph.
-A school has just purchased new computer equipment for $16,000.00. The graph shows the 259) depreciation of the equipment over 5 years. The point (0, 16,000) represents the purchase price and
The point (5, 0) represents when the equipment will be replaced. Find and interpret the average rate
Of change in cost per year.

Accepted Answer

A)  $3200 per year; the value of the equipment increases by $3200 per year during these years. 
B)  - $3200 per year; the value of the equipment decreases by $3200 per year during these years. 
C)  -$16,000 per year; the value of the equipment decreases by $16,000 per year during these years. 
D)  -$9600 per year; the value of the equipment decreases by $9600 per year during these years. 
A)  $3200 per year; the value of the equipment increases by $3200 per year during these years. 
B)  - $3200 per year; the value of the equipment decreases by $3200 per year during these years. 
C)  -$16,000 per year; the value of the equipment decreases by $16,000 per year during these years. 
D)  -$9600 per year; the value of the equipment decreases by $9600 per year during these years.

Question 7

Graph the line and give the domain and the range.
-$$2 x - 10 y = 0$$

Accepted Answer

A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , \quad R = ( - \infty , \infty )$
  
C)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , \quad R = ( - \infty , \infty )$
  
C)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 8

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x).
-$$h ( x ) = | 2 x + 4 |$$

Accepted Answer

A)  $f ( x ) = x , g ( x ) = 2 x + 4$ 
B)  $f ( x ) = | x | , g ( x ) = 2 x + 4$ 
C)  $f ( x ) = - | x | , g ( x ) = 2 x + 4$ 
D)  $f ( x ) = | - x | , g ( x ) = 2 x - 4$ 
A)  $f ( x ) = x , g ( x ) = 2 x + 4$ 
B)  $f ( x ) = | x | , g ( x ) = 2 x + 4$ 
C)  $f ( x ) = - | x | , g ( x ) = 2 x + 4$ 
D)  $f ( x ) = | - x | , g ( x ) = 2 x - 4$

Question 9

The graph of y = f(x) is given. Use the graph to find the function value.
-Find f(-5).

Accepted Answer

A)  5 
B)  2 
C)  -5 
D)  17 
A)  5 
B)  2 
C)  -5 
D)  17

Question 10

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $\{ 5,13 \}$; range: $\{ 4,7,12 \}$ 
B)  None of these 
C)  domain: $\{ 4,7,12 \}$; range: $\{ 5,13 \}$ 
D)  domain: $\{ 4,5,7 \}$; range: $\{ 12,13 \}$ 
A)  domain: $\{ 5,13 \}$; range: $\{ 4,7,12 \}$ 
B)  None of these 
C)  domain: $\{ 4,7,12 \}$; range: $\{ 5,13 \}$ 
D)  domain: $\{ 4,5,7 \}$; range: $\{ 12,13 \}$

Question 11

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing $( 5 , \infty )$; Decreasing $( - \infty , 5 )$ 
B)  Increasing $( - \infty , 5 )$; Decreasing $( 5 , \infty )$ 
C)  Increasing $( - \infty , 5 )$; Decreasing $( - \infty , 5 )$ 
D)  Increasing $( 5 , \infty )$; Decreasing $( 5 \infty )$ 
A)  Increasing $( 5 , \infty )$; Decreasing $( - \infty , 5 )$ 
B)  Increasing $( - \infty , 5 )$; Decreasing $( 5 , \infty )$ 
C)  Increasing $( - \infty , 5 )$; Decreasing $( - \infty , 5 )$ 
D)  Increasing $( 5 , \infty )$; Decreasing $( 5 \infty )$

Question 12

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$$f ( x ) = \frac { 1 } { 2 } x$$

Accepted Answer

A)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
C)  $D = ( - \infty , \infty ) , \quad R = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
A)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
B)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
C)  $D = ( - \infty , \infty ) , \quad R = ( - \infty , \infty )$
  
D)  $D = ( - \infty , \infty ) , R = ( - \infty , \infty )$

Question 13

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of
these.
-$$y = 7 x ^ { 5 } - 9 x ^ { 3 }$$

Accepted Answer

A)  origin only 
B)  $x$-axis, $y$-axis, origin 
C)  none of these 
D)  $y$-axis only 
A)  origin only 
B)  $x$-axis, $y$-axis, origin 
C)  none of these 
D)  $y$-axis only

Question 14

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept.
-

Accepted Answer

A)  $2 ; ( 0 , - 4 ) , ( 2,0 )$ 
B)  $2 ; ( 0,2 ) , ( - 4,0 )$ 
C)  $\frac { 1 } { 2 } ; ( 0 , - 4 ) , ( 2,0 )$ 
D)  $\frac { 1 } { 2 } ; ( 0,2 ) , ( - 4,0 )$ 
A)  $2 ; ( 0 , - 4 ) , ( 2,0 )$ 
B)  $2 ; ( 0,2 ) , ( - 4,0 )$ 
C)  $\frac { 1 } { 2 } ; ( 0 , - 4 ) , ( 2,0 )$ 
D)  $\frac { 1 } { 2 } ; ( 0,2 ) , ( - 4,0 )$

Question 15

Find the slope of the line satisfying the given conditions.
-through (-9, -1) and (-1, -1)

Accepted Answer

A)  -8 
B)  0 
C)  undefined 
D)  8 
A)  -8 
B)  0 
C)  undefined 
D)  8

Question 16

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 7 x + 4 } , g ( x ) = \frac { 1 } { x }$$
Find $( f - g ) ( x )$

Accepted Answer

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

Question 17

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
-Estimate B(7) and G(7) and use your estimates to estimate T(7).

Accepted Answer

A)  2.5; 4.0; 6.5 
B)  2.2; 4.3; 6.5 
C)  2.3; 4.0; 6.3 
D)  3.5; 4.2; 7.7 
A)  2.5; 4.0; 6.5 
B)  2.2; 4.3; 6.5 
C)  2.3; 4.0; 6.3 
D)  3.5; 4.2; 7.7

Question 18

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { 8 } { x + 4 } , \quad g ( x ) = \frac { 6 } { 5 x } \
( f \circ g ) ( x )
\end{array}$$

Accepted Answer

A)  $\frac { 40 x } { 6 - 20 x }$ 
B)  $\frac { 6 x + 24 } { 40 x }$ 
C)  $\frac { 8 x } { 6 + 20 x }$ 
D)  $\frac { 40 x } { 6 + 20 x }$ 
A)  $\frac { 40 x } { 6 - 20 x }$ 
B)  $\frac { 6 x + 24 } { 40 x }$ 
C)  $\frac { 8 x } { 6 + 20 x }$ 
D)  $\frac { 40 x } { 6 + 20 x }$

Question 19

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-$$y = 3 f ( x )$$

Accepted Answer

A)  $( 6,4 )$ 
B)  $( 2,6 )$ 
C)  $( 2,12 )$ 
D)  $( 5,2 )$ 
A)  $( 6,4 )$ 
B)  $( 2,6 )$ 
C)  $( 2,12 )$ 
D)  $( 5,2 )$

Question 20

Find the center-radius form of the circle described or graphed.
-A circle has a diameter with endpoints $( - 2,1 )$ and $( 22,11 )$. Find the radius.

Accepted Answer

A)  $\sqrt { 13 }$ 
B)  13 
C)  $\sqrt { 26 }$ 
D)  26 
A)  $\sqrt { 13 }$ 
B)  13 
C)  $\sqrt { 26 }$ 
D)  26

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }$

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = \frac { 2 } { x - 8 }$

The figure below shows the graph of a function y = f(x). Use this graph to - $\text { Sketch the graph of } y = - f ( x ) \text {. }$ $The figure below shows the graph of a function y = f(x). Use this graph to - \text { Sketch the graph of } y = - f ( x ) \text {. }$

Graph the line and give the domain and the range. - $3 y + 18 = 0$

Find the center-radius form of the circle described or graphed. -Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$ .

Graph the line and give the domain and the range. - $2 x - 10 y = 0$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = | 2 x + 4 |$

The graph of y = f(x) is given. Use the graph to find the function value. -Find f(-5).

Give the domain and range of the relation. -

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or none of these. - $y = 7 x ^ { 5 } - 9 x ^ { 3 }$

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

Find the slope of the line satisfying the given conditions. -through (-9, -1) and (-1, -1)

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 7 x + 4 } , g ( x ) = \frac { 1 } { x }$ Find $( f - g ) ( x )$

For the given functions f and g , find the indicated composition. - f(x)=,g(x)= (f\circg)(x)

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = 3 f ( x )$

Find the center-radius form of the circle described or graphed. -A circle has a diameter with endpoints $( - 2,1 )$ and $( 22,11 )$ . Find the radius.

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - f(x)=x3+8,g(x)=x−83f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }f(x)=x3+8,g(x)=3x−8​

Find the specified domain. -Find the domain of (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) when f(x)=2x−5f ( x ) = 2 x - 5f(x)=2x−5 and g(x)=2x−8g ( x ) = \frac { 2 } { x - 8 }g(x)=x−82​

The figure below shows the graph of a function y = f(x). Use this graph to - Sketch the graph of y=−f(x). \text { Sketch the graph of } y = - f ( x ) \text {. } Sketch the graph of y=−f(x).

Graph the line and give the domain and the range. - 3y+18=03 y + 18 = 03y+18=0

Find the center-radius form of the circle described or graphed. -Find the center-radius form of the equation of the circle having a diameter with endpoints (−5,1)( - 5,1 )(−5,1) and (3,7)( 3,7 )(3,7) .

Graph the line and give the domain and the range. - 2x−10y=02 x - 10 y = 02x−10y=0

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - h(x)=∣2x+4∣h ( x ) = | 2 x + 4 |h(x)=∣2x+4∣