Question 1

For the given functions f and g, find the requested function and state its domain.
-f(x) = 7x - 6; g(x) = 5x - 9 Find f - g.

Accepted Answer

A)  $( f - g ) ( x ) = 12 x - 15 ; \{ x \mid x \neq 1 \}$ 
B)  $( f - g ) ( x ) = 2 x - 15 ; \left\{ x \mid x \neq \frac { 15 } { 2 } \right\}$ 
C)  $( f - g ) ( x ) = - 2 x - 3$; all real numbers 
D)  $( f - g ) ( x ) = 2 x + 3$; all real numbers 
A)  $( f - g ) ( x ) = 12 x - 15 ; \{ x \mid x \neq 1 \}$ 
B)  $( f - g ) ( x ) = 2 x - 15 ; \left\{ x \mid x \neq \frac { 15 } { 2 } \right\}$ 
C)  $( f - g ) ( x ) = - 2 x - 3$; all real numbers 
D)  $( f - g ) ( x ) = 2 x + 3$; all real numbers

Question 2

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$$

Accepted Answer

A)  local maximum at (1, -4) 
B)  local maximum at (-1, 4) 
C)  local minimum at (1, 4) 
D)  local minimum at (-1, -4) 
A)  local maximum at (1, -4) 
B)  local maximum at (-1, 4) 
C)  local minimum at (1, 4) 
D)  local minimum at (-1, -4)

Question 3

Locate any intercepts of the function.
-$f ( x ) = \left\{ \begin{array} { l l } - 7 x + 8 & \text { if } x < 1 \ 8 x - 7 & \text { if } x \geq 1 \end{array} \right.$

Accepted Answer

A)  $( 0,8 )$ 
B)  $( 0 , - 7 )$ 
C)  $( 0,8 ) , \left( \frac { 8 } { 7 } , 0 \right) , \left( \frac { 7 } { 8 } , 0 \right)$ 
D)  $( 0 , - 7 ) , \left( \frac { 8 } { 7 } , 0 \right) , \left( \frac { 7 } { 8 } , 0 \right)$ 
A)  $( 0,8 )$ 
B)  $( 0 , - 7 )$ 
C)  $( 0,8 ) , \left( \frac { 8 } { 7 } , 0 \right) , \left( \frac { 7 } { 8 } , 0 \right)$ 
D)  $( 0 , - 7 ) , \left( \frac { 8 } { 7 } , 0 \right) , \left( \frac { 7 } { 8 } , 0 \right)$

Question 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.
-$f ( x ) = | x + 4 |-3$

Accepted Answer

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

Question 5

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = 2 + 8 x - x ^ { 2 } ; ( - 5,5 )$$

Accepted Answer

A)  local maximum at (-4, 50) 
B)  local minimum at (-4, 18) 
C)  local maximum at (4, 18) 
D)  local minimum at (4, 50) 
A)  local maximum at (-4, 50) 
B)  local minimum at (-4, 18) 
C)  local maximum at (4, 18) 
D)  local minimum at (4, 50)

Question 6

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
1 & \text { if } - 5 \leq x < - 1 \
| x | & \text { if } - 1 \leq x < 5 \
\sqrt { x } & \text { if } 5 \leq x \leq 27
\end{array} \right.$$

Accepted Answer

A)  {x| 5 ≤ x ≤ 27} 
B)  {x|-5 ≤ x ≤27} 
C)  {x|x ≥ -5} 
D)  {x|-5 ≤ x < 5 or 5 < x ≤27} 
A)  {x| 5 ≤ x ≤ 27} 
B)  {x|-5 ≤ x ≤27} 
C)  {x|x ≥ -5} 
D)  {x|-5 ≤ x < 5 or 5 < x ≤27}

Question 7

Solve the problem.
-Suppose that P(x) represents the percentage of income spent on housing in year x and I(x) represents income in year x. Determine a function H that represents total housing expenditures in year x.

Accepted Answer

A)  H(x) = (P · I)(x) 
B)  H(x) = (P + I)(x) 
C)  $$\mathrm { H } ( \mathrm { x } ) = \left( \frac { \mathrm { I } } { \mathrm { P } } \right) ( \mathrm { x } )$$ 
D)  H(x) = (I - P)(x) 
A)  H(x) = (P · I)(x) 
B)  H(x) = (P + I)(x) 
C)  $$\mathrm { H } ( \mathrm { x } ) = \left( \frac { \mathrm { I } } { \mathrm { P } } \right) ( \mathrm { x } )$$ 
D)  H(x) = (I - P)(x)

Question 8

Solve the problem.
-Express the gross salary G of a person who earns $40 per hour as a function of the number x of hours worked.

Accepted Answer

A)  $G ( x ) = \frac { 40 } { x }$ 
B)  $G ( x ) = 40 x ^ { 2 }$ 
C)  $G ( x ) = 40 x$ 
D)  $G ( x ) = 40 + x$ 
A)  $G ( x ) = \frac { 40 } { x }$ 
B)  $G ( x ) = 40 x ^ { 2 }$ 
C)  $G ( x ) = 40 x$ 
D)  $G ( x ) = 40 + x$

Question 9

Match the correct function to the graph.
-

Accepted Answer

A)  $y = - 2 x ^ { 2 }$ 
B)  $y = 1 - x ^ { 2 }$ 
C)  $y = - 2 x ^ { 2 } + 1$ 
D)  $y = - 2 x ^ { 2 } - 1$ 
A)  $y = - 2 x ^ { 2 }$ 
B)  $y = 1 - x ^ { 2 }$ 
C)  $y = - 2 x ^ { 2 } + 1$ 
D)  $y = - 2 x ^ { 2 } - 1$

Question 10

For the given functions f and g, find the requested function and state its domain.
-f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 3 } { 5 \mathrm { x } + 4 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 3 } { 5 } \right\}$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 3 } { 5 x + 4 } ; \left\{ x \mid x \neq - \frac { 4 } { 5 } \right\}$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 4 } { 5 x - 3 } ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 4 } { 5 \mathrm { x } - 3 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 4 } { 5 } \right\}$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 3 } { 5 \mathrm { x } + 4 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 3 } { 5 } \right\}$ 
B)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x - 3 } { 5 x + 4 } ; \left\{ x \mid x \neq - \frac { 4 } { 5 } \right\}$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 5 x + 4 } { 5 x - 3 } ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } + 4 } { 5 \mathrm { x } - 3 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 4 } { 5 } \right\}$

Question 11

The graph of a function f is given. Use the graph to answer the question.
-Is f(8) positive or negative?

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 12

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g.

Accepted Answer

A)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } , x \neq 4 \right\}$ 
B)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } \right\}$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \frac { 8 \mathrm { x } + 8 } { 9 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 9 } \right\}$ 
D)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \{ x \mid x \neq 0 \}$ 
A)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } , x \neq 4 \right\}$ 
B)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \left\{ x \mid x \neq \frac { 2 } { 9 } \right\}$ 
C)  $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \frac { 8 \mathrm { x } + 8 } { 9 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 9 } \right\}$ 
D)  $( f - g ) ( x ) = \frac { 2 x - 8 } { 9 x - 2 } ; \{ x \mid x \neq 0 \}$

Question 13

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of y =x. The graph is shifted up 4 units, reflected about the y-axis, and finally shifted left 3 units.

Accepted Answer

A)  $y = - \sqrt { x + 3 } + 4$ 
B)  $y = \sqrt { - x + 3 } - 4$ 
C)  $y = \sqrt { - x - 3 } + 4$ 
D)  $y = \sqrt { - x - 3 } - 4$ 
A)  $y = - \sqrt { x + 3 } + 4$ 
B)  $y = \sqrt { - x + 3 } - 4$ 
C)  $y = \sqrt { - x - 3 } + 4$ 
D)  $y = \sqrt { - x - 3 } - 4$

Question 14

Find the domain of the function.
-$$f ( x ) = - 4 x - 5$$

Accepted Answer

A)  {x|x > 0} 
B)  {x|x ≠ 0} 
C)  {x|x ≥ 5} 
D)  all real numbers 
A)  {x|x > 0} 
B)  {x|x ≠ 0} 
C)  {x|x ≥ 5} 
D)  all real numbers

Question 15

Solve the problem.
-The volume V of a square-based pyramid with base sides s and height h is V = 13 s2h. If the height is half of the
length of a base side, express the volume V as a function of s.

Accepted Answer

The answer of Solve the problem.
-The volume V of a...

Question 16

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6$; all real numbers 
B)  $( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers 
C)  $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers 
D)  $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}$ 
A)  $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6$; all real numbers 
B)  $( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers 
C)  $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers 
D)  $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}$

Question 17

Find the average rate of change for the function between the given values.
-$f ( x ) = \sqrt { 2 x - 1 } ; \text { from } 1 \text { to } 5$

Accepted Answer

A) $ \frac { 1 } { 2 }$ 
B)  -28 
C)   $- \frac { 1 } { 6 }$ 
D)  -2 
A) $ \frac { 1 } { 2 }$ 
B)  -28 
C)   $- \frac { 1 } { 6 }$ 
D)  -2

Question 18

The graph of a piecewise-defined function is given. Write a definition for the function.
-

Accepted Answer

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

Question 19

Find the average rate of change for the function between the given values.
-$f ( x ) = \frac { 3 } { x + 2 }$

Accepted Answer

A)  -2 
B)  -28 
C)  $ - \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  -2 
B)  -28 
C)  $ - \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 }$

Question 20

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-

Accepted Answer

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

For the given functions f and g, find the requested function and state its domain. -f(x) = 7x - 6; g(x) = 5x - 9 Find f - g.

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } - 7 x + 8 & \text { if } x < 1 \\ 8 x - 7 & \text { if } x \geq 1 \end{array} \right.$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = | x + 4 |-3$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = 2 + 8 x - x ^ { 2 } ; ( - 5,5 )$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } - 5 \leq x < - 1 \\| x | & \text { if } - 1 \leq x < 5 \\\sqrt { x } & \text { if } 5 \leq x \leq 27\end{array} \right.$

Solve the problem. -Suppose that P(x) represents the percentage of income spent on housing in year x and I(x) represents income in year x. Determine a function H that represents total housing expenditures in year x.

Solve the problem. -Express the gross salary G of a person who earns $40 per hour as a function of the number x of hours worked.

Match the correct function to the graph. -

For the given functions f and g, find the requested function and state its domain. -f(x) = 5x + 4; g(x) = 5x - 3 $\text { Find } \frac { \mathrm { f } } { \mathrm { g } } \text {. }$

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 5 x - 8 } { 9 x - 2 } ; g ( x ) = \frac { 3 x } { 9 x - 2 }$ Find f - g.

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y =x. The graph is shifted up 4 units, reflected about the y-axis, and finally shifted left 3 units.

Find the domain of the function. - $f ( x ) = - 4 x - 5$

Solve the problem. -The volume V of a square-based pyramid with base sides s and height h is V = 13 s2h. If the height is half of the length of a base side, express the volume V as a function of s.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$ Find $f \cdot g$ .

Find the average rate of change for the function between the given values. - $f ( x ) = \sqrt { 2 x - 1 } ; \text { from } 1 \text { to } 5$

The graph of a piecewise-defined function is given. Write a definition for the function. -

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x + 2 }$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

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Exam 1: Functions and Their Graphs