Question 1

Find the requested composition of functions.
-Given $f ( x ) = 2 x ^ { 2 } - 3$ and $g ( x ) = \frac { 3 } { x }$, find $f g ( x )$.

Accepted Answer

A)  $\frac { 18 } { x ^ { 2 } } - 3$ 
B)  $6 x - \frac { 9 } { x }$ 
C)  $\frac { 3 } { 2 x ^ { 2 } - 3 }$ 
D)  $\frac { 18 } { x } - 3$ 
A)  $\frac { 18 } { x ^ { 2 } } - 3$ 
B)  $6 x - \frac { 9 } { x }$ 
C)  $\frac { 3 } { 2 x ^ { 2 } - 3 }$ 
D)  $\frac { 18 } { x } - 3$

Question 2

Find the inverse of the relation.
-$$\{ ( 6,0 ) , ( - 4,1 ) , ( - 6,2 ) , ( - 8,3 ) \}$$

Accepted Answer

A)  $\{ ( 1,0 ) , ( 3 , - 6 ) , ( 6 , - 6 ) , ( 1,2 ) \}$ 
B)  $\{ ( 0,6 ) , ( 1 , - 4 ) , ( 2 , - 6 ) , ( 3 , - 8 ) \}$ 
C)  $\{ ( 1,0 ) , ( 0 , - 6 ) , ( 6 , - 4 ) , ( 1,2 ) \}$ 
A)  $\{ ( 1,0 ) , ( 3 , - 6 ) , ( 6 , - 6 ) , ( 1,2 ) \}$ 
B)  $\{ ( 0,6 ) , ( 1 , - 4 ) , ( 2 , - 6 ) , ( 3 , - 8 ) \}$ 
C)  $\{ ( 1,0 ) , ( 0 , - 6 ) , ( 6 , - 4 ) , ( 1,2 ) \}$

Question 3

Determine whether the function is one-to-one.
-$$f ( x ) = 6 x ^ { 3 } - 2$$

Accepted Answer

A) True 
 B)False

Question 4

Find the inverse of the relation.
-$$\{ ( - 8 , - 7 ) , ( 7,8 ) , ( - 4 , - 3 ) , ( 4,3 ) \}$$

Accepted Answer

A)  $\{ ( 3 , - 4 ) , ( - 4,7 ) , ( - 7 , - 8 ) , ( - 3,4 ) \}$ 
B)  $\{ ( - 7 , - 8 ) , ( 8,7 ) , ( - 3 , - 4 ) , ( 3,4 ) \}$ 
C)  $\{ ( 3 , - 4 ) , ( 8,7 ) , ( - 7,7 ) , ( - 3,4 ) \}$ 
A)  $\{ ( 3 , - 4 ) , ( - 4,7 ) , ( - 7 , - 8 ) , ( - 3,4 ) \}$ 
B)  $\{ ( - 7 , - 8 ) , ( 8,7 ) , ( - 3 , - 4 ) , ( 3,4 ) \}$ 
C)  $\{ ( 3 , - 4 ) , ( 8,7 ) , ( - 7,7 ) , ( - 3,4 ) \}$

Question 5

Find an equation of the inverse of the relation.
-$$y = 2 x ^ { 3 } + 6$$

Accepted Answer

A)  $y = - 2 x ^ { 3 } - 6$ 
B)  $x = 2 y ^ { 3 } + 6$ 
C)  $x = 6 y ^ { 3 } + 2$ 
D)  $y = 6 x ^ { 3 } + 2$ 
A)  $y = - 2 x ^ { 3 } - 6$ 
B)  $x = 2 y ^ { 3 } + 6$ 
C)  $x = 6 y ^ { 3 } + 2$ 
D)  $y = 6 x ^ { 3 } + 2$

Question 6

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table: 
$\begin{array} { l | l } 
\text { Year } & \text { Profits } \
\hline 1996 & \$ 250,000 \
1997 & \$ 300,000 \
1998 & \$ 400,000 \
1999 & \$ 600,000
\end{array}$

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimat profits. Use the linear graph to estimate the profits in the year $2002 .$

Accepted Answer

A)  About $\$ 800,000$ 
B)  About $\$ 500,000$ 
C)  About $\$ 1,000,000$ 
D)  About $\$ 900,000$ 
A)  About $\$ 800,000$ 
B)  About $\$ 500,000$ 
C)  About $\$ 1,000,000$ 
D)  About $\$ 900,000$

Question 7

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = 4 x + 3$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 3 } { 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 4 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 4 } - 3$ 
D)  Not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = \frac { x + 3 } { 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 4 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 4 } - 3$ 
D)  Not a one-to-one function

Question 8

Find f(x)and g(x)such that h(x)= (f ° g)(x).
-$$h ( x ) = ( \sqrt { x } - 5 ) ^ { 5 }$$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } , g ( x ) = \sqrt { x } - 5$ 
B)  $f ( x ) = \sqrt { x ^ { 5 } } , g ( x ) = x - 5$ 
C)  $f ( x ) = \sqrt { x } - 5 , g ( x ) = x ^ { 5 }$ 
D)  $f ( x ) = \sqrt { x } , g ( x ) = ( x - 5 ) ^ { 5 }$ 
A)  $f ( x ) = x ^ { 5 } , g ( x ) = \sqrt { x } - 5$ 
B)  $f ( x ) = \sqrt { x ^ { 5 } } , g ( x ) = x - 5$ 
C)  $f ( x ) = \sqrt { x } - 5 , g ( x ) = x ^ { 5 }$ 
D)  $f ( x ) = \sqrt { x } , g ( x ) = ( x - 5 ) ^ { 5 }$

Question 9

Solve the problem.
-The half-life of a certain radioactive substance is 8 years. Suppose that at time $t = 0$, there are $29 \mathrm {~g}$ of the substance. Then after t years, the number of grams of the substance remaining will be:
$$N ( t ) = 29 \left( \frac { 1 } { 2 } \right) ^ { t / 16 }$$
How many grams of the substance will remain after 56 years? Round to the nearest hundredth when necessary.

Accepted Answer

A)  $0.64 \mathrm {~g}$ 
B)  $1.28 \mathrm {~g}$ 
C)  $0.32 \mathrm {~g}$ 
D)  $2.56 \mathrm {~g}$ 
A)  $0.64 \mathrm {~g}$ 
B)  $1.28 \mathrm {~g}$ 
C)  $0.32 \mathrm {~g}$ 
D)  $2.56 \mathrm {~g}$

Question 10

Find the inverse of the relation.
-$$\{ ( - 16,3 ) , ( 5 , - 16 ) , ( - 14 , - 12 ) \}$$

Accepted Answer

A)  $\{ ( - 16 , - 16 ) , ( - 16,5 ) , ( - 12 , - 14 ) \}$ 
B)  $\{ ( 3 , - 16 ) , ( - 16,5 ) , ( - 12 , - 14 ) \}$ 
C)  $\{ ( 3 , - 16 ) , ( - 14,5 ) , ( - 12 , - 16 ) \}$ 
A)  $\{ ( - 16 , - 16 ) , ( - 16,5 ) , ( - 12 , - 14 ) \}$ 
B)  $\{ ( 3 , - 16 ) , ( - 16,5 ) , ( - 12 , - 14 ) \}$ 
C)  $\{ ( 3 , - 16 ) , ( - 14,5 ) , ( - 12 , - 16 ) \}$

Question 11

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
-$$y = 2 + 3 x$$

Accepted Answer

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

Question 12

Find the inverse of the relation.
-$$\{ ( - 5 , - 4 ) , ( 5,4 ) , ( - 3,6 ) , ( 3 , - 6 ) \}$$

Accepted Answer

A)  $\{ ( - 4 , - 5 ) , ( 4,5 ) , ( 6,5 ) , ( - 6,3 ) \}$ 
B)  $\{ ( - 4 , - 5 ) , ( 4,5 ) , ( 6 , - 3 ) , ( - 6,3 ) \}$ 
C)  $\{ ( - 4 , - 5 ) , ( - 5,5 ) , ( 6 , - 3 ) , ( - 6,3 ) \}$ 
A)  $\{ ( - 4 , - 5 ) , ( 4,5 ) , ( 6,5 ) , ( - 6,3 ) \}$ 
B)  $\{ ( - 4 , - 5 ) , ( 4,5 ) , ( 6 , - 3 ) , ( - 6,3 ) \}$ 
C)  $\{ ( - 4 , - 5 ) , ( - 5,5 ) , ( 6 , - 3 ) , ( - 6,3 ) \}$

Question 13

Graph.
-$f(x)=\left(\frac{1}{2}\right)^{x}$

Accepted Answer

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

Question 14

Find f(x)and g(x)such that h(x)= (f ° g)(x).
-$$h ( x ) = \frac { 6 } { \sqrt { 10 x + 7 } }$$

Accepted Answer

A)  $f ( x ) = 6 , g ( x ) = \sqrt { 10 + 7 }$ 
B)  $f ( x ) = \sqrt { 10 x + 7 } , g ( x ) = 6$ 
C)  $f ( x ) = \frac { 6 } { \sqrt { x } } , g ( x ) = 10 x + 7$ 
D)  $f ( x ) = \frac { 6 } { x } , g ( x ) = 10 x + 7$ 
A)  $f ( x ) = 6 , g ( x ) = \sqrt { 10 + 7 }$ 
B)  $f ( x ) = \sqrt { 10 x + 7 } , g ( x ) = 6$ 
C)  $f ( x ) = \frac { 6 } { \sqrt { x } } , g ( x ) = 10 x + 7$ 
D)  $f ( x ) = \frac { 6 } { x } , g ( x ) = 10 x + 7$

Question 15

Graph.
-$f(x)=4^{x}-3$

Accepted Answer

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

Question 16

Solve the problem.
-An accountant tabulated a firm's profits for four recent years in the following table: 
$\begin{array} { l | l } 
\text { Year } & \text { Profits } \
\hline 1996 & \$ 250,000 \
1997 & \$ 300,000 \
1998 & \$ 400,000 \
1999 & \$ 600,000
\end{array}$

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimat profits. Use the exponential graph to estimate the profits in the year $2001 .$

Accepted Answer

A)  About $\$ 750,000$ 
B)  About $\$ 300,000$ 
C)  About $\$ 1,300,000$ 
D)  About $\$ 1,000,000$ 
A)  About $\$ 750,000$ 
B)  About $\$ 300,000$ 
C)  About $\$ 1,300,000$ 
D)  About $\$ 1,000,000$

Question 17

Solve the problem.
-The amount of particulate matter left in solution during a filtering process decreases by the equation $\mathrm { P } ( \mathrm { n } ) = 700 ( 0.5 ) ^ { 0.6 \mathrm { n } }$, where $\mathrm { n }$ is the number of filtering steps. Find the amounts left for $\mathrm { n } = 0$ and $\mathrm { n } = 5$. (Round to the nearest whole number.)

Accepted Answer

A)  $700 ; 22$ 
B)  $700 ; 88$ 
C)  $1400 ; 88$ 
D)  $700 ; 5600$ 
A)  $700 ; 22$ 
B)  $700 ; 88$ 
C)  $1400 ; 88$ 
D)  $700 ; 5600$

Question 18

Find f(x)and g(x)such that h(x)= (f ° g)(x).
-$$h ( x ) = ( 9 x + 9 ) ^ { 7 }$$

Accepted Answer

A)  $f ( x ) = ( 9 x ) ^ { 7 } , g ( x ) = 9$ 
B)  $f ( x ) = 9 x + 9 , g ( x ) = x ^ { 7 }$ 
C)  $f ( x ) = 9 x ^ { 7 } , g ( x ) = x + 9$ 
D)  $f ( x ) = x ^ { 7 } , g ( x ) = 9 x + 9$ 
A)  $f ( x ) = ( 9 x ) ^ { 7 } , g ( x ) = 9$ 
B)  $f ( x ) = 9 x + 9 , g ( x ) = x ^ { 7 }$ 
C)  $f ( x ) = 9 x ^ { 7 } , g ( x ) = x + 9$ 
D)  $f ( x ) = x ^ { 7 } , g ( x ) = 9 x + 9$

Question 19

Solve the problem.
-Suppose that $\$ 40,000$ is invested at $6 \%$ interest, compounded annually. Find a function A for the amount in the account after $t$ years.

Accepted Answer

A)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ^ { 0.06 \mathrm { t } }$ 
B)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ( 1.06 ) ^ { \mathrm { t } }$ 
C)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ^ { 1.06 t }$ 
D)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ( 0.06 ) ^ { t }$ 
A)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ^ { 0.06 \mathrm { t } }$ 
B)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ( 1.06 ) ^ { \mathrm { t } }$ 
C)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ^ { 1.06 t }$ 
D)  $\mathrm { A } ( \mathrm { t } ) = \$ 40,000 ( 0.06 ) ^ { t }$

Question 20

Determine whether the given function is one-to-one. If so, find a formula for the inverse.
-$$f ( x ) = \frac { 4 } { x + 5 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { - 5 x + 4 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 + 4 x } { x }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 5 + 4 x }$ 
A)  $f ^ { - 1 } ( x ) = \frac { - 5 x + 4 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 + 4 x } { x }$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 5 + 4 x }$

Find the requested composition of functions. -Given $f ( x ) = 2 x ^ { 2 } - 3$ and $g ( x ) = \frac { 3 } { x }$ , find $f g ( x )$ .

Find the inverse of the relation. - $\{ ( 6,0 ) , ( - 4,1 ) , ( - 6,2 ) , ( - 8,3 ) \}$

Determine whether the function is one-to-one. - $f ( x ) = 6 x ^ { 3 } - 2$

Find the inverse of the relation. - $\{ ( - 8 , - 7 ) , ( 7,8 ) , ( - 4 , - 3 ) , ( 4,3 ) \}$

Find an equation of the inverse of the relation. - $y = 2 x ^ { 3 } + 6$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 4 x + 3$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = ( \sqrt { x } - 5 ) ^ { 5 }$

Find the inverse of the relation. - $\{ ( - 16,3 ) , ( 5 , - 16 ) , ( - 14 , - 12 ) \}$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - $y = 2 + 3 x$

Find the inverse of the relation. - $\{ ( - 5 , - 4 ) , ( 5,4 ) , ( - 3,6 ) , ( 3 , - 6 ) \}$

Graph. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph. - f(x)=\left(\frac{1}{2}\right)^{x}$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \frac { 6 } { \sqrt { 10 x + 7 } }$

Graph. - $f(x)=4^{x}-3$ $Graph. - f(x)=4^{x}-3$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = ( 9 x + 9 ) ^ { 7 }$

Solve the problem. -Suppose that $\$ 40,000$ is invested at $6 \%$ interest, compounded annually. Find a function A for the amount in the account after $t$ years.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \frac { 4 } { x + 5 }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 12: Exponential Functions and Logarithmic Functions

Find the requested composition of functions. -Given f(x)=2x2−3f ( x ) = 2 x ^ { 2 } - 3f(x)=2x2−3 and g(x)=3xg ( x ) = \frac { 3 } { x }g(x)=x3​ , find fg(x)f g ( x )fg(x) .

Find the inverse of the relation. - {(6,0),(−4,1),(−6,2),(−8,3)}\{ ( 6,0 ) , ( - 4,1 ) , ( - 6,2 ) , ( - 8,3 ) \}{(6,0),(−4,1),(−6,2),(−8,3)}

Determine whether the function is one-to-one. - f(x)=6x3−2f ( x ) = 6 x ^ { 3 } - 2f(x)=6x3−2

Find the inverse of the relation. - {(−8,−7),(7,8),(−4,−3),(4,3)}\{ ( - 8 , - 7 ) , ( 7,8 ) , ( - 4 , - 3 ) , ( 4,3 ) \}{(−8,−7),(7,8),(−4,−3),(4,3)}

Find an equation of the inverse of the relation. - y=2x3+6y = 2 x ^ { 3 } + 6y=2x3+6

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=4x+3f ( x ) = 4 x + 3f(x)=4x+3

Find f(x)and g(x)such that h(x)= (f ° g)(x). - h(x)=(x−5)5h ( x ) = ( \sqrt { x } - 5 ) ^ { 5 }h(x)=(x​−5)5

Find the inverse of the relation. - {(−16,3),(5,−16),(−14,−12)}\{ ( - 16,3 ) , ( 5 , - 16 ) , ( - 14 , - 12 ) \}{(−16,3),(5,−16),(−14,−12)}

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - y=2+3xy = 2 + 3 xy=2+3x

Find the inverse of the relation. - {(−5,−4),(5,4),(−3,6),(3,−6)}\{ ( - 5 , - 4 ) , ( 5,4 ) , ( - 3,6 ) , ( 3 , - 6 ) \}{(−5,−4),(5,4),(−3,6),(3,−6)}

Graph. - f(x)=(12)xf(x)=\left(\frac{1}{2}\right)^{x}f(x)=(21​)x

Find f(x)and g(x)such that h(x)= (f ° g)(x). - h(x)=610x+7h ( x ) = \frac { 6 } { \sqrt { 10 x + 7 } }h(x)=10x+7​6​

Graph. - f(x)=4x−3f(x)=4^{x}-3f(x)=4x−3

Find f(x)and g(x)such that h(x)= (f ° g)(x). - h(x)=(9x+9)7h ( x ) = ( 9 x + 9 ) ^ { 7 }h(x)=(9x+9)7

Solve the problem. -Suppose that $40,000\$ 40,000$40,000 is invested at 6%6 \%6% interest, compounded annually. Find a function A for the amount in the account after ttt years.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - f(x)=4x+5f ( x ) = \frac { 4 } { x + 5 }f(x)=x+54​

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Find the requested composition of functions. -Given $f ( x ) = 2 x ^ { 2 } - 3$ and $g ( x ) = \frac { 3 } { x }$ , find $f g ( x )$ .

Find the inverse of the relation. - $\{ ( 6,0 ) , ( - 4,1 ) , ( - 6,2 ) , ( - 8,3 ) \}$

Determine whether the function is one-to-one. - $f ( x ) = 6 x ^ { 3 } - 2$

Find the inverse of the relation. - $\{ ( - 8 , - 7 ) , ( 7,8 ) , ( - 4 , - 3 ) , ( 4,3 ) \}$

Find an equation of the inverse of the relation. - $y = 2 x ^ { 3 } + 6$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = 4 x + 3$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = ( \sqrt { x } - 5 ) ^ { 5 }$

Find the inverse of the relation. - $\{ ( - 16,3 ) , ( 5 , - 16 ) , ( - 14 , - 12 ) \}$

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - $y = 2 + 3 x$

Find the inverse of the relation. - $\{ ( - 5 , - 4 ) , ( 5,4 ) , ( - 3,6 ) , ( 3 , - 6 ) \}$

Graph. - $f(x)=\left(\frac{1}{2}\right)^{x}$ $Graph. - f(x)=\left(\frac{1}{2}\right)^{x}$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \frac { 6 } { \sqrt { 10 x + 7 } }$

Graph. - $f(x)=4^{x}-3$ $Graph. - f(x)=4^{x}-3$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = ( 9 x + 9 ) ^ { 7 }$

Solve the problem. -Suppose that $\$ 40,000$ is invested at $6 \%$ interest, compounded annually. Find a function A for the amount in the account after $t$ years.

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \frac { 4 } { x + 5 }$