Question 1

State the domain and range of the function.
-$$f ( x ) = - 5 ^ { - x } - 4$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , - 5 )$ 
C)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , - 4 )$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , - 4 )$ 
A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , - 5 )$ 
C)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , - 4 )$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , - 4 )$

Question 2

Solve the problem.
-On a circle of radius 12 meters, how long is an arc that subtends a central angle of $140 ^ { \circ }$ ?

Accepted Answer

A)  $\frac { 28 \pi } { 3 } \mathrm {~m}$ 
B)  $1680 \pi \mathrm { m }$ 
C)  $\frac { 28 } { 3 } \mathrm {~m}$ 
D)  $1680 \mathrm {~m}$ 
A)  $\frac { 28 \pi } { 3 } \mathrm {~m}$ 
B)  $1680 \pi \mathrm { m }$ 
C)  $\frac { 28 } { 3 } \mathrm {~m}$ 
D)  $1680 \mathrm {~m}$

Question 3

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = \left| x ^ { 2 } - 7 \right|$$

Accepted Answer

A)  $[ - 10,10 ]$ by $[ - 15,15 ]$ 
B)  $[ - 5,5 ]$ by $[ - 2,10 ]$ 
C)  $[ - 5,5 ]$ by $[ - 15,15 ]$ 
D)  $[ 0,5 ]$ by $[ - 2,10 ]$ 
A)  $[ - 10,10 ]$ by $[ - 15,15 ]$ 
B)  $[ - 5,5 ]$ by $[ - 2,10 ]$ 
C)  $[ - 5,5 ]$ by $[ - 15,15 ]$ 
D)  $[ 0,5 ]$ by $[ - 2,10 ]$

Question 4

Graph the function.
-$f(x)=4(x-3)$

Accepted Answer

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

Question 5

Solve the problem.
-If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 2 }$, and $h ( x ) = 2 x + 4$, find $f ( g ( h ( x ) ) )$.

Accepted Answer

A)  $2 \sqrt { x } + 4$ 
B)  $\sqrt { x + 4 }$ 
C)  $\sqrt { x } + 2$ 
D)  $\sqrt { x + 2 }$ 
A)  $2 \sqrt { x } + 4$ 
B)  $\sqrt { x + 4 }$ 
C)  $\sqrt { x } + 2$ 
D)  $\sqrt { x + 2 }$

Question 6

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$e ^ { 8 x } e ^ { 7 x } = e ^ { 7 }$$

Accepted Answer

A)  -1.443 
B)  2.377 
C)  0.467 
D)  0.594 
A)  -1.443 
B)  2.377 
C)  0.467 
D)  0.594

Question 7

Find the domain and graph the function.
-$G ( t ) = \frac { 1 } { | t - 3 | }$

Accepted Answer

A)  $\mathrm { D } : ( - \infty , 0 ) \cup ( 0 , \infty )$
  
B)  D: $( - \infty , 3 ) \cup ( 3 , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , 3 ) \cup ( 3 , \infty )$
  
A)  $\mathrm { D } : ( - \infty , 0 ) \cup ( 0 , \infty )$
  
B)  D: $( - \infty , 3 ) \cup ( 3 , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , 3 ) \cup ( 3 , \infty )$

Question 8

Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = ( - 3 x + 18 ) ^ { 8 }$$

Accepted Answer

A)  $f ( x ) = - 3 x ^ { 8 } , g ( x ) = x + 18$ 
B)  $f ( x ) = ( - 3 x ) ^ { 8 } , g ( x ) = 18$ 
C)  $f ( x ) = - 3 x + 18 , g ( x ) = x ^ { 8 }$ 
D)  $f ( x ) = x ^ { 8 } , g ( x ) = - 3 x + 18$ 
A)  $f ( x ) = - 3 x ^ { 8 } , g ( x ) = x + 18$ 
B)  $f ( x ) = ( - 3 x ) ^ { 8 } , g ( x ) = 18$ 
C)  $f ( x ) = - 3 x + 18 , g ( x ) = x ^ { 8 }$ 
D)  $f ( x ) = x ^ { 8 } , g ( x ) = - 3 x + 18$

Question 9

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = \sqrt { 7 + 6 x - x ^ { 2 } }$$

Accepted Answer

A)  $[ - 10,10 ]$ by $[ - 10,5 ]$ 
B)  $[ - 4,5 ]$ by $[ - 15,25 ]$ 
C)  $[ - 10,20 ]$ by $[ - 50,50 ]$ 
D)  $[ - 4,5 ]$ by $[ - 5,5 ]$ 
A)  $[ - 10,10 ]$ by $[ - 10,5 ]$ 
B)  $[ - 4,5 ]$ by $[ - 15,25 ]$ 
C)  $[ - 10,20 ]$ by $[ - 50,50 ]$ 
D)  $[ - 4,5 ]$ by $[ - 5,5 ]$

Question 10

Solve the problem.
-In the formula N $$\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }$$ N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a
Certain country to double if its annual growth rate is 6.9%? Round to the nearest year.

Accepted Answer

A)  29 yr 
B)  1 yr 
C)  10 yr 
D)  4 yr 
A)  29 yr 
B)  1 yr 
C)  10 yr 
D)  4 yr

Question 11

Solve the problem.
-Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Accepted Answer

A)  1.89 yr 
B)  18.94 yr 
C)  51.72 yr 
D)  0.19 yr 
A)  1.89 yr 
B)  18.94 yr 
C)  51.72 yr 
D)  0.19 yr

Question 12

Find the requested information using the law of cosines and/or the law of sines. Round to three decimal places.
-A triangle has sides $a = 3$ and $b = 4$ and angle $C = 40 ^ { \circ }$. Find the sine of $B$.

Accepted Answer

A)  $0.25$ 
B)  $0.062$ 
C)  $0.75$ 
D)  1 
A)  $0.25$ 
B)  $0.062$ 
C)  $0.75$ 
D)  1

Question 13

Express the following logarithm as specified.
-$\ln 2 \sqrt { 2 }$ in terms of $\ln 2$ and $\ln 3$

Accepted Answer

A)  $\ln 3 + \frac { \ln 2 } { 2 }$ 
B)  $\frac { \ln 2 } { 2 }$ 
C)  $\frac { 3 } { 2 } \ln 2$ 
D)  $\ln 2 + \frac { \ln 2 } { 2 }$ 
A)  $\ln 3 + \frac { \ln 2 } { 2 }$ 
B)  $\frac { \ln 2 } { 2 }$ 
C)  $\frac { 3 } { 2 } \ln 2$ 
D)  $\ln 2 + \frac { \ln 2 } { 2 }$

Question 14

Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = \frac { 1 } { x ^ { 2 } - 5 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 5 }$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 5$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 5$ 
D)  $f ( x ) = \frac { 1 } { 5 } , g ( x ) = x ^ { 2 } - 5$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 5 }$ 
B)  $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 5$ 
C)  $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 5$ 
D)  $f ( x ) = \frac { 1 } { 5 } , g ( x ) = x ^ { 2 } - 5$

Question 15

State the domain and range of the function.
-$$f ( x ) = 3 e ^ { - x } - 2$$

Accepted Answer

A)  domain: $( - \infty , 0 )$; range: $( - \infty , - 2 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( - 2 , \infty )$ 
A)  domain: $( - \infty , 0 )$; range: $( - \infty , - 2 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( - 2 , \infty )$

Question 16

Solve for t or y, as appropriate.
-$\mathrm { e } ^ { \mathrm { t } / 550 } = \mathrm { k }$

Accepted Answer

A)  $\ln 550 \mathrm { k }$ 
B)  $550 \ln \mathrm { k }$ 
C)  $550 \mathrm { e } ^ { \mathrm { k } }$ 
D)  $\frac { \ln \mathrm { k } } { 550 }$ 
A)  $\ln 550 \mathrm { k }$ 
B)  $550 \ln \mathrm { k }$ 
C)  $550 \mathrm { e } ^ { \mathrm { k } }$ 
D)  $\frac { \ln \mathrm { k } } { 550 }$

Question 17

Solve the problem.
-If $f ( x ) = \frac { 1 } { x }$ and $g ( x ) = 2 x ^ { 2 }$, find $g ( f ( x ) )$.

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $\frac { 2 } { x }$ 
C)  $\frac { 1 } { 2 x ^ { 2 } }$ 
D)  $\frac { 2 } { x ^ { 2 } }$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $\frac { 2 } { x }$ 
C)  $\frac { 1 } { 2 x ^ { 2 } }$ 
D)  $\frac { 2 } { x ^ { 2 } }$

Question 18

Solve for the angle , where 0 2
-$$\sin ^ { 2 } \theta = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $\theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
C)  $\theta = 0 , \pi , 2 \pi$ 
D)  $\theta = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $\theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
C)  $\theta = 0 , \pi , 2 \pi$ 
D)  $\theta = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }$

Question 19

Simplify the expression.
-$4^{\log _{4}(2 x)}$

Accepted Answer

A)  $2 x$ 
B)  4 
C)  $4 ^ { 2 x }$ 
D)  1 
A)  $2 x$ 
B)  4 
C)  $4 ^ { 2 x }$ 
D)  1

Question 20

Solve for t or y, as appropriate.
-$$\ln ( y - 6 ) - \ln 10 = x + \ln x$$

Accepted Answer

A)  $e ^ { x } + 10 x + 6$ 
B)  $10 x e ^ { x } + 6$ 
C)  $2 x + 16$ 
D)  $( x + 10 ) \mathrm { e } ^ { x } + 6$ 
A)  $e ^ { x } + 10 x + 6$ 
B)  $10 x e ^ { x } + 6$ 
C)  $2 x + 16$ 
D)  $( x + 10 ) \mathrm { e } ^ { x } + 6$

State the domain and range of the function. - $f ( x ) = - 5 ^ { - x } - 4$

Solve the problem. -On a circle of radius 12 meters, how long is an arc that subtends a central angle of $140 ^ { \circ }$ ?

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = \left| x ^ { 2 } - 7 \right|$

Graph the function. - $f(x)=4(x-3)$

Solve the problem. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 2 }$ , and $h ( x ) = 2 x + 4$ , find $f ( g ( h ( x ) ) )$ .

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $e ^ { 8 x } e ^ { 7 x } = e ^ { 7 }$

Find the domain and graph the function. - $G ( t ) = \frac { 1 } { | t - 3 | }$ $Find the domain and graph the function. - G ( t ) = \frac { 1 } { | t - 3 | }$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = ( - 3 x + 18 ) ^ { 8 }$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = \sqrt { 7 + 6 x - x ^ { 2 } }$

Solve the problem. -Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Find the requested information using the law of cosines and/or the law of sines. Round to three decimal places. -A triangle has sides $a = 3$ and $b = 4$ and angle $C = 40 ^ { \circ }$ . Find the sine of $B$ .

Express the following logarithm as specified. - $\ln 2 \sqrt { 2 }$ in terms of $\ln 2$ and $\ln 3$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = \frac { 1 } { x ^ { 2 } - 5 }$

State the domain and range of the function. - $f ( x ) = 3 e ^ { - x } - 2$

Solve for t or y, as appropriate. - $\mathrm { e } ^ { \mathrm { t } / 550 } = \mathrm { k }$

Solve the problem. -If $f ( x ) = \frac { 1 } { x }$ and $g ( x ) = 2 x ^ { 2 }$ , find $g ( f ( x ) )$ .

Solve for the angle , where 0 2 - $\sin ^ { 2 } \theta = \frac { 1 } { 4 }$

Simplify the expression. - $4^{\log _{4}(2 x)}$

Solve for t or y, as appropriate. - $\ln ( y - 6 ) - \ln 10 = x + \ln x$

Limits and Continuity

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Applications of Derivatives

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Exam 2: Functions

State the domain and range of the function. - f(x)=−5−x−4f ( x ) = - 5 ^ { - x } - 4f(x)=−5−x−4

Solve the problem. -On a circle of radius 12 meters, how long is an arc that subtends a central angle of 140∘140 ^ { \circ }140∘ ?

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - f(x)=∣x2−7∣f ( x ) = \left| x ^ { 2 } - 7 \right|f(x)=​x2−7​

Graph the function. - f(x)=4(x−3)f(x)=4(x-3)f(x)=4(x−3)

Solve the problem. -If f(x)=x,g(x)=x2f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 2 }f(x)=x​,g(x)=2x​ , and h(x)=2x+4h ( x ) = 2 x + 4h(x)=2x+4 , find f(g(h(x)))f ( g ( h ( x ) ) )f(g(h(x))) .

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - e8xe7x=e7e ^ { 8 x } e ^ { 7 x } = e ^ { 7 }e8xe7x=e7

Find the domain and graph the function. - G(t)=1∣t−3∣G ( t ) = \frac { 1 } { | t - 3 | }G(t)=∣t−3∣1​

Express the given function as a composite of functions f and g such that y y=f(g(x))y = f ( g ( x ) )y=f(g(x)) - y=(−3x+18)8y = ( - 3 x + 18 ) ^ { 8 }y=(−3x+18)8

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - f(x)=7+6x−x2f ( x ) = \sqrt { 7 + 6 x - x ^ { 2 } }f(x)=7+6x−x2​