Question 1

Decide whether or not the functions are inverses of each other.
-$f ( x ) = 3 x + 9 , g ( x ) = \frac { 1 } { 3 } x - 3$

Accepted Answer

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

Question 2

A balloon (in the shape of a sphere) is being inflated. The radius is increasing at a rate of  4 cm  per second. Find a function,  r(t) , for the radius in terms of  t . Find a function,  V(r) , for the volume of the balloon in terms of r . Find $\left( \mathrm { V } { } ^ { \circ } \mathrm { r } \right) ( \mathrm { t } )$

Accepted Answer

A)  $( \mathrm { V } \cdot \mathrm { r } ) ( \mathrm { t } ) = \frac { 320 \pi \mathrm { t } ^ { 2 } } { 3 }$ 
B)  $\left( V { } ^ { \circ } r \right) ( t ) = \frac { 112 \pi t ^ { 3 } } { 3 }$ 
C)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 256 \pi t ^ { 3 } } { 3 }$ 
D)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 1024 \pi \sqrt { \mathrm { t } } } { 3 }$ 
A)  $( \mathrm { V } \cdot \mathrm { r } ) ( \mathrm { t } ) = \frac { 320 \pi \mathrm { t } ^ { 2 } } { 3 }$ 
B)  $\left( V { } ^ { \circ } r \right) ( t ) = \frac { 112 \pi t ^ { 3 } } { 3 }$ 
C)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 256 \pi t ^ { 3 } } { 3 }$ 
D)  $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 1024 \pi \sqrt { \mathrm { t } } } { 3 }$

Question 3

Determine whether or not the function is one-to-one.
-$$f ( x ) = \sqrt { 16 - x ^ { 2 } }$$

Accepted Answer

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

Question 4

For the functions f and g, find the requested value.
-Evaluate $( g \circ f ) ( - 2 )$.
$y=f(x)$

$y=g(x)$

Accepted Answer

A)  $- 2$ 
B)  1 
C)  2 
D)  $- 0.5$ 
A)  $- 2$ 
B)  1 
C)  2 
D)  $- 0.5$

Question 5

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of  4.1  feet per second. Find a function,  d(t) , which gives the distance Ken is from the streetlight in terms of time. Find a function,  S(d), which gives the length of Ken's shadow in terms of d. Then find $( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } )$

Accepted Answer

A)  
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 2.26 \mathrm { t }$ 
B)  
$( S \circ \mathrm { d } ) ( \mathrm { t } ) = 6.93 \mathrm { t }$ 
C)  
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 3.9 \mathrm { t }$ 
D) 
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 3.08 \mathrm { t }$ 
A)  
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 2.26 \mathrm { t }$ 
B)  
$( S \circ \mathrm { d } ) ( \mathrm { t } ) = 6.93 \mathrm { t }$ 
C)  
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 3.9 \mathrm { t }$ 
D) 
$( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } ) = 3.08 \mathrm { t }$

Question 6

Write the equation of the graph after the indicated transformation(s).
-The graph of $y = x ^ { 2 }$ is shifted 5 units to the left and 4 units downward.

Accepted Answer

A)  $y = ( x - 5 ) ^ { 2 } - 4$ 
B)  $y = ( x + 5 ) ^ { 2 } - 4$ 
C)  $y = ( x + 4 ) ^ { 2 } - 5$ 
D)  $y = ( x - 4 ) ^ { 2 } + 5$ 
A)  $y = ( x - 5 ) ^ { 2 } - 4$ 
B)  $y = ( x + 5 ) ^ { 2 } - 4$ 
C)  $y = ( x + 4 ) ^ { 2 } - 5$ 
D)  $y = ( x - 4 ) ^ { 2 } + 5$

Question 7

Assume that the profit P made when  t  units are sold, $t > 0$ is given by $P ( t ) = t ^ { 2 } - 28 t + 180$ For what values of t will there be a loss (that is, $\mathrm { P } < 0 \}$ ?

Accepted Answer

A)   t=10  or  t=18 
B)  $0  18$ 
C)  $10  0$ 
A)   t=10  or  t=18 
B)  $0  18$ 
C)  $10  0$

Question 8

Solve the inequality.
-$x ^ { 2 } + 10 x + 24 \geq 0$

Accepted Answer

A)  $- 6 \leq x \leq - 4$ 
B)  $x \leq - 6$ 
C)  $x \geq - 4$ 
D)  $x \leq - 6 \text { or } x \geq - 4$ 
A)  $- 6 \leq x \leq - 4$ 
B)  $x \leq - 6$ 
C)  $x \geq - 4$ 
D)  $x \leq - 6 \text { or } x \geq - 4$

Question 9

Provide an appropriate response.
-Why does the horizontal line test (checking if a function is one-to-one) work?

Accepted Answer

Answers may vary. One possibility: any t

Question 10

Find the inverse of the function.
-$f ( x ) = - x ^ { 2 } + 12 , x \geq 0$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { 12 - \mathrm { x } }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 12$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 12 }$ 
D)  $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 12 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { 12 - \mathrm { x } }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 12$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 12 }$ 
D)  $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 12 }$

Question 11

Determine the values of x for which f(x) and g(x) are inverse functions.
-$$f ( x ) = ( x - 13 ) ^ { 2 } + 4 , g ( x ) = \sqrt { x - 4 } + 13$$

Accepted Answer

A)  $x \geq 0$ 
B)  $x \geq 13$ 
C)  $x \leq 0$ 
D)  $x \geq 4$ 
A)  $x \geq 0$ 
B)  $x \geq 13$ 
C)  $x \leq 0$ 
D)  $x \geq 4$

Question 12

If f is a one-to-one function and the graph of f lies completely within the first quadrant, then the
graph of f-1 lies completely within the first quadrant.

Accepted Answer

A) True 
 B)False

Question 13

Sketch the graph of the pair of functions. Use a dashed line for g(x)
-$f(x)=|x|, \quad g(x)=|x-2|$

Accepted Answer

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

Question 14

Determine whether the function is even, odd, or neither.
-$f ( x ) = 0.83 x ^ { 2 } + | x | - 1$

Accepted Answer

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

Question 15

Determine whether the function is even, odd, or neither.
-$f ( x ) = ( x + 5 ) ( x + 9 )$

Accepted Answer

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

Question 16

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality.
-$f(x)>0$

Accepted Answer

A)  $x  3$ 
B)  $- 4 < x < 3$ 
C)  no solution 
D)  $x < - 4$ 
A)  $x  3$ 
B)  $- 4 < x < 3$ 
C)  no solution 
D)  $x < - 4$

Question 17

Use the quadratic formula or graphing methods to
-$$2 x ^ { 2 } + 10 x + 4 \leq 0$$

Accepted Answer

A)  $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
B)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ 
C)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ or $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
D)  $\frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562 \leq x \leq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
A)  $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
B)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ 
C)  $x \leq \frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562$ or $x \geq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$ 
D)  $\frac { - 5 - \sqrt { 17 } } { 2 } \approx - 4.562 \leq x \leq \frac { - 5 + \sqrt { 17 } } { 2 } \approx - 0.438$

Question 18

The height  h  of a ball thrown is given by $h ( x ) = 2 x - 0.08 x ^ { 2 }$ where  x  is the horizontal distance traveled and both measurements are in feet. At what horizontal distances will the height of the ball be more than  9 ft  ? (Round distances to the nearest tenth of a foot, if necessary.)

Accepted Answer

A)  $0 \mathrm { ft } < \mathrm { x } < 5.9 \mathrm { ft } \text { or } 19.1 \mathrm { ft } < \mathrm { x } < 25 \mathrm { ft }$ 
B)  $0 \mathrm { ft } < \mathrm { x } < 19.1 \mathrm { ft }$ 
C)  $5.9 \mathrm { ft } < \mathrm { x } < 25 \mathrm { ft }$ 
D)  $5.9 \mathrm { ft } < \mathrm { x } < 19.1 \mathrm { ft }$ 
A)  $0 \mathrm { ft } < \mathrm { x } < 5.9 \mathrm { ft } \text { or } 19.1 \mathrm { ft } < \mathrm { x } < 25 \mathrm { ft }$ 
B)  $0 \mathrm { ft } < \mathrm { x } < 19.1 \mathrm { ft }$ 
C)  $5.9 \mathrm { ft } < \mathrm { x } < 25 \mathrm { ft }$ 
D)  $5.9 \mathrm { ft } < \mathrm { x } < 19.1 \mathrm { ft }$

Question 19

Determine if the complete graph represents a function that is even, odd, or neither.
-

Accepted Answer

A)  even 
B)  neither 
C)  odd 
A)  even 
B)  neither 
C)  odd

Question 20

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse.
-$$\{ ( - 8,2 ) , ( 18,2 ) , ( - 10,13 ) \}$$

Accepted Answer

A)  $\{ ( - 8,2 ) , ( 2,18 ) , ( 13 , - 10 ) \}$ 
B)  $\{ ( 2 , - 8 ) , ( - 10,18 ) , ( 13,2 ) \}$ 
C)  No inverse 
D)  $\{ ( 2 , - 8 ) , ( 2,18 ) , ( 13 , - 10 ) \}$ 
A)  $\{ ( - 8,2 ) , ( 2,18 ) , ( 13 , - 10 ) \}$ 
B)  $\{ ( 2 , - 8 ) , ( - 10,18 ) , ( 13,2 ) \}$ 
C)  No inverse 
D)  $\{ ( 2 , - 8 ) , ( 2,18 ) , ( 13 , - 10 ) \}$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 3 x + 9 , g ( x ) = \frac { 1 } { 3 } x - 3$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { 16 - x ^ { 2 } }$

Write the equation of the graph after the indicated transformation(s). -The graph of $y = x ^ { 2 }$ is shifted 5 units to the left and 4 units downward.

Assume that the profit P made when t units are sold, $t > 0$ is given by $P ( t ) = t ^ { 2 } - 28 t + 180$ For what values of t will there be a loss (that is, $\mathrm { P } < 0 \}$ ?

Solve the inequality. - $x ^ { 2 } + 10 x + 24 \geq 0$

Provide an appropriate response. -Why does the horizontal line test (checking if a function is one-to-one) work?

Find the inverse of the function. - $f ( x ) = - x ^ { 2 } + 12 , x \geq 0$

Determine the values of x for which f(x) and g(x) are inverse functions. - $f ( x ) = ( x - 13 ) ^ { 2 } + 4 , g ( x ) = \sqrt { x - 4 } + 13$

If f is a one-to-one function and the graph of f lies completely within the first quadrant, then the graph of f-1 lies completely within the first quadrant.

Sketch the graph of the pair of functions. Use a dashed line for g(x) - $f(x)=|x|, \quad g(x)=|x-2|$ $Sketch the graph of the pair of functions. Use a dashed line for g(x) - f(x)=|x|, \quad g(x)=|x-2|$

Determine whether the function is even, odd, or neither. - $f ( x ) = 0.83 x ^ { 2 } + | x | - 1$

Determine whether the function is even, odd, or neither. - $f ( x ) = ( x + 5 ) ( x + 9 )$

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $f(x)>0$ $Use the given graph of f(x) f ( x ) = a x ^ { 2 } + b x + c c to solve the specified inequality. - f(x)>0$

Use the quadratic formula or graphing methods to - $2 x ^ { 2 } + 10 x + 4 \leq 0$

The height h of a ball thrown is given by $h ( x ) = 2 x - 0.08 x ^ { 2 }$ where x is the horizontal distance traveled and both measurements are in feet. At what horizontal distances will the height of the ball be more than 9 ft ? (Round distances to the nearest tenth of a foot, if necessary.)

Determine if the complete graph represents a function that is even, odd, or neither. -

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - $\{ ( - 8,2 ) , ( 18,2 ) , ( - 10,13 ) \}$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

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Exam 4: Additional Topics With Functions

Decide whether or not the functions are inverses of each other. - f(x)=3x+9,g(x)=13x−3f ( x ) = 3 x + 9 , g ( x ) = \frac { 1 } { 3 } x - 3f(x)=3x+9,g(x)=31​x−3

Determine whether or not the function is one-to-one. - f(x)=16−x2f ( x ) = \sqrt { 16 - x ^ { 2 } }f(x)=16−x2​

For the functions f and g, find the requested value. -Evaluate (g∘f)(−2)( g \circ f ) ( - 2 )(g∘f)(−2) . y=f(x)y=f(x)y=f(x) y=g(x)y=g(x)y=g(x)

Write the equation of the graph after the indicated transformation(s). -The graph of y=x2y = x ^ { 2 }y=x2 is shifted 5 units to the left and 4 units downward.

Assume that the profit P made when t units are sold, t>0t > 0t>0 is given by P(t)=t2−28t+180P ( t ) = t ^ { 2 } - 28 t + 180P(t)=t2−28t+180 For what values of t will there be a loss (that is, P<0}\mathrm { P } < 0 \}P<0} ?

Solve the inequality. - x2+10x+24≥0x ^ { 2 } + 10 x + 24 \geq 0x2+10x+24≥0