Question 1

Use the quadratic formula or graphing methods to
-$$9 x ^ { 2 } \geq 3 - 3 x$$

Accepted Answer

A)  $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$ 
B)  $\frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768 \leq x \leq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$ 
C)  $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$ 
D)  $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$ or $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$ 
A)  $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$ 
B)  $\frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768 \leq x \leq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$ 
C)  $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$ 
D)  $x \leq \frac { - 1 - \sqrt { 13 } } { 6 } \approx - 0.768$ or $x \geq \frac { - 1 + \sqrt { 13 } } { 6 } \approx 0.434$

Question 2

Determine whether or not the function is one-to-one.
-

Accepted Answer

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

Question 3

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.
-$(x)=x^{3}+2$

Accepted Answer

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

Question 4

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$\begin{array}{l}
\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 2 & 22 \
\hline 10 & - 4 \
\hline 11 & - 12 \
\hline 21 & 20
\end{array}\\
\begin{array} { l | l } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline & \
\hline & \
\hline & \
\hline &
\end{array}
\end{array}$

Accepted Answer

A) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 2 & 20 \
\hline 10 & 22 \
\hline 11 & - 4 \
\hline 21 & - 12
\end{array}$ 
B) $\text { Not one-to-one }$ 
C) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 22 & 2 \
\hline - 4 & 10 \
\hline - 12 & 21 \
\hline 20 & 11
\end{array}$ 
D) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 22 & 2 \
\hline - 4 & 10 \
\hline - 12 & 11 \
\hline 20 & 21
\end{array}$ 
A) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 2 & 20 \
\hline 10 & 22 \
\hline 11 & - 4 \
\hline 21 & - 12
\end{array}$ 
B) $\text { Not one-to-one }$ 
C) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 22 & 2 \
\hline - 4 & 10 \
\hline - 12 & 21 \
\hline 20 & 11
\end{array}$ 
D) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 22 & 2 \
\hline - 4 & 10 \
\hline - 12 & 11 \
\hline 20 & 21
\end{array}$

Question 5

For the functions f and g, find the requested value.
-$$\text { Evaluate } ( f \circ g ) ( 1 ) \text {. }$$
$y=f(x)$

$y=g(x)$

Accepted Answer

A)  3 
B)  2 
C)  5 
D)  1 
A)  3 
B)  2 
C)  5 
D)  1

Question 6

An organization determines that the cost per person of chartering a bus is given by the formula $C ( x ) = \frac { 200 + 7 x } { x }$
where  x  is the number of people in the group and  C(x)  is in dollars. Find a formula for the inverse of this functio

Accepted Answer

A)  $C ^ { - 1 } ( x ) = \frac { 200 } { x + 7 }$ 
B)  $C ^ { - 1 } ( x ) = \frac { 7 } { x - 200 }$ 
C)  $C ^ { - 1 } ( x ) = \frac { 200 } { x - 7 }$ 
D)  $C ^ { - 1 } ( x ) = \frac { 200 + x } { 7 }$ 
A)  $C ^ { - 1 } ( x ) = \frac { 200 } { x + 7 }$ 
B)  $C ^ { - 1 } ( x ) = \frac { 7 } { x - 200 }$ 
C)  $C ^ { - 1 } ( x ) = \frac { 200 } { x - 7 }$ 
D)  $C ^ { - 1 } ( x ) = \frac { 200 + x } { 7 }$

Question 7

Determine whether (f(g(x)) $$( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$$
-$f ( x ) = x ^ { 2 } + 5 , g ( x ) = \sqrt { x } - 5$

Accepted Answer

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

Question 8

At Allied Electronics, production has begun on the X-15 Computer Chip. The total cost function is given by  C(x)=3 x+10  and the total profit function is given by $P ( x ) = - 0.3 x ^ { 2 } + 44 x - 10$ where  x  represents the number of boxes of computer chips produced. The total revenue function,  R(x) , is such that  R(x)=C(x)+P(x) . Find  R(x) .

Accepted Answer

A)  $R ( x ) = 49 x - 0.3 x ^ { 2 }$ 
B)  $R ( x ) = 47 x - 0.3 x ^ { 2 }$ 
C)  $R ( x ) = 46 x - 0.6 x ^ { 2 }$ 
D)  $R ( x ) = 47 x + 0.3 x ^ { 2 }$ 
A)  $R ( x ) = 49 x - 0.3 x ^ { 2 }$ 
B)  $R ( x ) = 47 x - 0.3 x ^ { 2 }$ 
C)  $R ( x ) = 46 x - 0.6 x ^ { 2 }$ 
D)  $R ( x ) = 47 x + 0.3 x ^ { 2 }$

Question 9

The linear equation  y=229 x+6320  provides an approximation of the annual cost (in dollars) to rent an apartment at the Leisure Village Retirement Community, where  x=1  represents 2011,  x=2  represents 2012, and so on. Write an equation that yields the same y-values when the exact year number is entered.

Accepted Answer

A)   y=229(x-2010)+6320 
B)   y=229(2010-x)+6320 
C)   y=229(2011-x)+6320 
D)   y=229(x-2011)+6320 
A)   y=229(x-2010)+6320 
B)   y=229(2010-x)+6320 
C)   y=229(2011-x)+6320 
D)   y=229(x-2011)+6320

Question 10

Solve the equation
-$6 x ^ { 2 / 5 } + 11 x ^ { 1 / 5 } + 4 = 0$

Accepted Answer

A)  - $\frac { 1024 } { 243 } , - \frac { 1 } { 32 }$ 
B)  $\frac { 1024 } { 243 } , \frac { 1 } { 32 }$ 
C)  3,2 
D)  - $\frac { 4 } { 3 } , - \frac { 1 } { 2 }$ 
A)  - $\frac { 1024 } { 243 } , - \frac { 1 } { 32 }$ 
B)  $\frac { 1024 } { 243 } , \frac { 1 } { 32 }$ 
C)  3,2 
D)  - $\frac { 4 } { 3 } , - \frac { 1 } { 2 }$

Question 11

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse.
-$$\{ ( 1 , - 3 ) , ( 2 , - 3 ) , ( 3,4 ) , ( 4 , - 4 ) \}$$

Accepted Answer

A)  No inverse 
B)  $\{ ( 1 , - 4 ) , ( 1,4 ) , ( 3,2 ) \}$ 
C)  $\{ ( - 3,1 ) , ( - 4,4 ) , ( 3,2 ) \}$ 
D)  $\{ ( - 3,1 ) , ( 2,4 ) , ( 3 , - 4 ) \}$ 
A)  No inverse 
B)  $\{ ( 1 , - 4 ) , ( 1,4 ) , ( 3,2 ) \}$ 
C)  $\{ ( - 3,1 ) , ( - 4,4 ) , ( 3,2 ) \}$ 
D)  $\{ ( - 3,1 ) , ( 2,4 ) , ( 3 , - 4 ) \}$

Question 12

Find the requested composition of functions.
-Given $f ( x ) = \frac { x - 7 } { 10 }$ and $g ( x ) = 10 x + 7$, find $( g \circ f ) ( x )$

Accepted Answer

A)  $x + 14$ 
B)  $x$ 
C)  $x - \frac { 7 } { 10 }$ 
D)  $10 x + 63$ 
A)  $x + 14$ 
B)  $x$ 
C)  $x - \frac { 7 } { 10 }$ 
D)  $10 x + 63$

Question 13

Provide an appropriate response.
-Why does a linear function always have an inverse?

Accepted Answer

Answers will vary. One possibility: actu

Question 14

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines
the inverse. If not, explain why not.
-

Accepted Answer

A)  Yes; 
B)  No; the function is not one-to-one.

Question 15

Determine whether or not the function is one-to-one.
-$f ( x ) = \frac { 7 } { x - 6 }$

Accepted Answer

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

Question 16

The graph of the function y $y = f ( x ) \text { is given. On the same axes, sketch the graph of } f ^ { - 1 } ( x )$ . Use a dashed line for the inverse
function.
-

Accepted Answer

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

Question 17

Determine whether or not the function is one-to-one.
-$f ( x ) = 8 x ^ { 3 } - 1$

Accepted Answer

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

Question 18

Find the requested function value.
-Find $( g \circ f ) ( - 28 )$ when $f ( x ) = \frac { x - 4 } { 8 }$ and $g ( x ) = 8 x + 8$

Accepted Answer

A)  $- \frac { 55 } { 2 }$ 
B)  $- 24$ 
C)  $- 64$ 
D)  864 
A)  $- \frac { 55 } { 2 }$ 
B)  $- 24$ 
C)  $- 64$ 
D)  864

Question 19

The monthly total cost of producing clock radios is given by  C(x)=34,000+29x , where  x  is the number of radios produced per month. Find the monthly average cost function.

Accepted Answer

A)  $\bar { C } ( x ) = \frac { x } { 34,000 + 29 x }$ 
B)  $\bar { C } ( x ) = \frac { 34,000 + 29 x } { x }$ 
C)  $\bar { C } ( x ) = \frac { 34,000 + 29 } { x }$ 
D)  $\bar { C } ( x ) = x ( 34,000 + 29 x )$ 
A)  $\bar { C } ( x ) = \frac { x } { 34,000 + 29 x }$ 
B)  $\bar { C } ( x ) = \frac { 34,000 + 29 x } { x }$ 
C)  $\bar { C } ( x ) = \frac { 34,000 + 29 } { x }$ 
D)  $\bar { C } ( x ) = x ( 34,000 + 29 x )$

Question 20

Determine whether (f(g(x)) $$( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$$
-$f ( x ) = x ^ { 3 } + 9 , g ( x ) = \sqrt [ 3 ] { x - 9 }$

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

Use the quadratic formula or graphing methods to - $9 x ^ { 2 } \geq 3 - 3 x$

Determine whether or not the function is one-to-one. -

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $(x)=x^{3}+2$ $Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - (x)=x^{3}+2$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - () 2 22 10 -4 11 -12 21 20 ()

An organization determines that the cost per person of chartering a bus is given by the formula $C ( x ) = \frac { 200 + 7 x } { x }$ where x is the number of people in the group and C(x) is in dollars. Find a formula for the inverse of this functio

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = x ^ { 2 } + 5 , g ( x ) = \sqrt { x } - 5$

Solve the equation - $6 x ^ { 2 / 5 } + 11 x ^ { 1 / 5 } + 4 = 0$

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - $\{ ( 1 , - 3 ) , ( 2 , - 3 ) , ( 3,4 ) , ( 4 , - 4 ) \}$

Find the requested composition of functions. -Given $f ( x ) = \frac { x - 7 } { 10 }$ and $g ( x ) = 10 x + 7$ , find $( g \circ f ) ( x )$

Provide an appropriate response. -Why does a linear function always have an inverse?

Determine if the function f defined by the arrow diagram has an inverse. If it does, create an arrow diagram that defines the inverse. If not, explain why not. -

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { 7 } { x - 6 }$

Determine whether or not the function is one-to-one. - $f ( x ) = 8 x ^ { 3 } - 1$

Find the requested function value. -Find $( g \circ f ) ( - 28 )$ when $f ( x ) = \frac { x - 4 } { 8 }$ and $g ( x ) = 8 x + 8$

The monthly total cost of producing clock radios is given by C(x)=34,000+29x , where x is the number of radios produced per month. Find the monthly average cost function.

Determine whether (f(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$ - $f ( x ) = x ^ { 3 } + 9 , g ( x ) = \sqrt [ 3 ] { x - 9 }$

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

Special Topics in Algebra

Filters

Exam 4: Additional Topics With Functions

Use the quadratic formula or graphing methods to - 9x2≥3−3x9 x ^ { 2 } \geq 3 - 3 x9x2≥3−3x

Determine whether or not the function is one-to-one. -

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - (x)=x3+2(x)=x^{3}+2(x)=x3+2

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - () 2 22 10 -4 11 -12 21 20 ()

For the functions f and g, find the requested value. - Evaluate (f∘g)(1). \text { Evaluate } ( f \circ g ) ( 1 ) \text {. } Evaluate (f∘g)(1). y=f(x)y=f(x)y=f(x) y=g(x)y=g(x)y=g(x)

An organization determines that the cost per person of chartering a bus is given by the formula C(x)=200+7xxC ( x ) = \frac { 200 + 7 x } { x }C(x)=x200+7x​ where x is the number of people in the group and C(x) is in dollars. Find a formula for the inverse of this functio

Determine whether (f(g(x)) (f(g(x))=x and whether (g(f(x))=x( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x(f(g(x))=x and whether (g(f(x))=x - f(x)=x2+5,g(x)=x−5f ( x ) = x ^ { 2 } + 5 , g ( x ) = \sqrt { x } - 5f(x)=x2+5,g(x)=x​−5

Solve the equation - 6x2/5+11x1/5+4=06 x ^ { 2 / 5 } + 11 x ^ { 1 / 5 } + 4 = 06x2/5+11x1/5+4=0

Determine if the function f defined by the set of ordered pairs has an inverse. If so, find the inverse. - {(1,−3),(2,−3),(3,4),(4,−4)}\{ ( 1 , - 3 ) , ( 2 , - 3 ) , ( 3,4 ) , ( 4 , - 4 ) \}{(1,−3),(2,−3),(3,4),(4,−4)}

Find the requested composition of functions. -Given f(x)=x−710f ( x ) = \frac { x - 7 } { 10 }f(x)=10x−7​ and g(x)=10x+7g ( x ) = 10 x + 7g(x)=10x+7 , find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)