Question 1

State the period of the function and graph.
-$-\sin \left(\frac{\pi x}{3}\right)$

Accepted Answer

A)  Period 6
  
B)  Period 6
  
C)  Period 6
  
D)  Period 6
  
A)  Period 6
  
B)  Period 6
  
C)  Period 6
  
D)  Period 6

Question 2

Solve the problem.
-If $f ( x ) = 4 x ^ { 2 } + 2 x + 3$ and $g ( x ) = 2 x - 7$, find $g ( f ( x ) )$.

Accepted Answer

A)  $4 x ^ { 2 } + 2 x - 4$ 
B)  $8 x ^ { 2 } + 4 x - 1$ 
C)  $4 x ^ { 2 } + 4 x - 1$ 
D)  $8 x ^ { 2 } + 4 x + 13$ 
A)  $4 x ^ { 2 } + 2 x - 4$ 
B)  $8 x ^ { 2 } + 4 x - 1$ 
C)  $4 x ^ { 2 } + 4 x - 1$ 
D)  $8 x ^ { 2 } + 4 x + 13$

Question 3

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 10% compounded annually for 8 years

Accepted Answer

A)  $1357.95 
B)  $948.72 
C)  $1143.59 
D)  $2143.59 
A)  $1357.95 
B)  $948.72 
C)  $1143.59 
D)  $2143.59

Question 4

Find the domain and range of the function.
-$g ( z ) = 2 - \sqrt { z }$

Accepted Answer

A)  D: $( - \infty , 0 ] , R : [ 2 , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $( - \infty , 2 ]$ 
C)  D: $( - \infty , 2 ]$, R: $( - \infty , \infty )$ 
D)  D: $[ 0 , \infty ) , R : ( - \infty , 2 ]$ 
A)  D: $( - \infty , 0 ] , R : [ 2 , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $( - \infty , 2 ]$ 
C)  D: $( - \infty , 2 ]$, R: $( - \infty , \infty )$ 
D)  D: $[ 0 , \infty ) , R : ( - \infty , 2 ]$

Question 5

Use the appropriate addition formula to find the exact value of the expression.
-$\tan \left( \frac { 7 \pi } { 12 } \right)$

Accepted Answer

A)  $2 + \sqrt { 3 }$ 
B)  $\frac { 2 + \sqrt { 3 } } { 4 }$ 
C)  $- 2 - \sqrt { 3 }$ 
D)  $\frac { 2 - \sqrt { 3 } } { 4 }$ 
A)  $2 + \sqrt { 3 }$ 
B)  $\frac { 2 + \sqrt { 3 } } { 4 }$ 
C)  $- 2 - \sqrt { 3 }$ 
D)  $\frac { 2 - \sqrt { 3 } } { 4 }$

Question 6

Graph the function.
-$y=|x+2|+7$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 7

Solve the problem.
-In the formula N $$\mathrm { N } = \mathrm { Ie } \mathrm { kt }$$ 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. There are currently 65 million cars in a certain
Country, increasing by 1.7% annually. How many years will it take for this country to have 81 million cars?
Round to the nearest year.

Accepted Answer

A)  9 yr 
B)  4 yr 
C)  13 yr 
D)  163 yr 
A)  9 yr 
B)  4 yr 
C)  13 yr 
D)  163 yr

Question 8

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$5 ( 3 x - 1 ) = 21$$

Accepted Answer

A)  0.964 
B)  0.297 
C)  1.733 
D)  0.812 
A)  0.964 
B)  0.297 
C)  1.733 
D)  0.812

Question 9

Solve for the angle , where 0 2
-$$\sin ^ { 2 } \theta = \frac { 3 } { 4 }$$

Accepted Answer

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

Question 10

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$13 ^ { 3 - x } = 21$$

Accepted Answer

A)  3.842 
B)  -1.385 
C)  1.385 
D)  1.813 
A)  3.842 
B)  -1.385 
C)  1.385 
D)  1.813

Question 11

Use the appropriate addition formula to find the exact value of the expression.
-$\sin \left( \frac { 11 \pi } { 12 } \right)$

Accepted Answer

A)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$ 
A)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$

Question 12

Using the graph below, find the domain and range of the given function, and sketch the graph.  
-$y=f(x+2)-1$

Accepted Answer

A)  D: $[ - 4,5 ] ; R : [ - 3,3 ]$
  
B)  D: $[ - 5,4 ] ; R : [ - 3,3 ]$
  
C)  D: $[ - 8,1 ] ; \mathrm { R } : [ - 2.5,5 ]$
  
D)  D: $[ - 7,2 ] ;$ R: $[ - 4,2 ]$
  
A)  D: $[ - 4,5 ] ; R : [ - 3,3 ]$
  
B)  D: $[ - 5,4 ] ; R : [ - 3,3 ]$
  
C)  D: $[ - 8,1 ] ; \mathrm { R } : [ - 2.5,5 ]$
  
D)  D: $[ - 7,2 ] ;$ R: $[ - 4,2 ]$

Question 13

Find the exact function value.
-$\sec ^ { - 1 } ( \sqrt { 2 } )$

Accepted Answer

A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { \pi } { 4 } \pm 2 \pi n , \frac { 7 \pi } { 4 } \pm 2 \pi n$ 
A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { \pi } { 4 }$ 
D)  $\frac { \pi } { 4 } \pm 2 \pi n , \frac { 7 \pi } { 4 } \pm 2 \pi n$

Question 14

Is the function graphed below one-to-one?
-

Accepted Answer

A) True 
 B)False

Question 15

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$$\left( 8 ^ { - 6 } \right) ^ { - 3 }$$

Accepted Answer

A)  $8 ^ { 9 }$ 
B)  $8 ^ { 18 }$ 
C)  $\frac { 1 } { 8 ^ { 18 } }$ 
D)  $\frac { 1 } { 8 ^ { 9 } }$ 
A)  $8 ^ { 9 }$ 
B)  $8 ^ { 18 }$ 
C)  $\frac { 1 } { 8 ^ { 18 } }$ 
D)  $\frac { 1 } { 8 ^ { 9 } }$

Question 16

Solve the problem.
-You want to make an angle measuring $110 ^ { \circ }$ by marking an arc on the perimeter of a disk with a diameter of 10 inches and drawing lines from the ends of the arc to the disk's center. To the nearest tenth of an inch, how long should the arc be?

Accepted Answer

A)  $4.8 \mathrm { in }$. 
B)  $19.2 \mathrm { in }$. 
C)  $38.4 \mathrm { in }$. 
D)  $9.6 \mathrm { in }$. 
A)  $4.8 \mathrm { in }$. 
B)  $19.2 \mathrm { in }$. 
C)  $38.4 \mathrm { in }$. 
D)  $9.6 \mathrm { in }$.

Question 17

Determine an appropriate viewing window for the given function and use it to display its graph.
-$y = 8 \sqrt { \frac { 9 + x ^ { 2 } } { 9 } }$

Accepted Answer

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

Question 18

Solve for t or y, as appropriate.
-$$e ^ { \sqrt { t } } = x ^ { 5 }$$

Accepted Answer

A)  $\left( \ln x ^ { 10 } \right)$ 
B)  $25 ( \ln x ) ^ { 2 }$ 
C)  $\sqrt { 5 \ln x }$ 
D)  $\mathrm { x } ^ { 10 }$ 
A)  $\left( \ln x ^ { 10 } \right)$ 
B)  $25 ( \ln x ) ^ { 2 }$ 
C)  $\sqrt { 5 \ln x }$ 
D)  $\mathrm { x } ^ { 10 }$

Question 19

Graph the function.
-$y=\left|x^{2}-2\right|$

Accepted Answer

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

Question 20

Solve the problem.
-The variable s is proportional to t, and s = 40 when t = 120. Determine t when s = 65.

Accepted Answer

A)  195 
B)  3 
C)  185 
D)  260 
A)  195 
B)  3 
C)  185 
D)  260

State the period of the function and graph. - $-\sin \left(\frac{\pi x}{3}\right)$ $State the period of the function and graph. - -\sin \left(\frac{\pi x}{3}\right)$

Solve the problem. -If $f ( x ) = 4 x ^ { 2 } + 2 x + 3$ and $g ( x ) = 2 x - 7$ , find $g ( f ( x ) )$ .

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 10% compounded annually for 8 years

Find the domain and range of the function. - $g ( z ) = 2 - \sqrt { z }$

Use the appropriate addition formula to find the exact value of the expression. - $\tan \left( \frac { 7 \pi } { 12 } \right)$

Graph the function. - $y=|x+2|+7$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ( 3 x - 1 ) = 21$

Solve for the angle , where 0 2 - $\sin ^ { 2 } \theta = \frac { 3 } { 4 }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $13 ^ { 3 - x } = 21$

Use the appropriate addition formula to find the exact value of the expression. - $\sin \left( \frac { 11 \pi } { 12 } \right)$

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=f(x+2)-1$

Find the exact function value. - $\sec ^ { - 1 } ( \sqrt { 2 } )$

Is the function graphed below one-to-one? -

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\left( 8 ^ { - 6 } \right) ^ { - 3 }$

Solve the problem. -You want to make an angle measuring $110 ^ { \circ }$ by marking an arc on the perimeter of a disk with a diameter of 10 inches and drawing lines from the ends of the arc to the disk's center. To the nearest tenth of an inch, how long should the arc be?

Determine an appropriate viewing window for the given function and use it to display its graph. - $y = 8 \sqrt { \frac { 9 + x ^ { 2 } } { 9 } }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - y = 8 \sqrt { \frac { 9 + x ^ { 2 } } { 9 } }$

Solve for t or y, as appropriate. - $e ^ { \sqrt { t } } = x ^ { 5 }$

Graph the function. - $y=\left|x^{2}-2\right|$ $Graph the function. - y=\left|x^{2}-2\right|$

Solve the problem. -The variable s is proportional to t, and s = 40 when t = 120. Determine t when s = 65.

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Exam 2: Functions

State the period of the function and graph. - −sin⁡(πx3)-\sin \left(\frac{\pi x}{3}\right)−sin(3πx​)

Solve the problem. -If f(x)=4x2+2x+3f ( x ) = 4 x ^ { 2 } + 2 x + 3f(x)=4x2+2x+3 and g(x)=2x−7g ( x ) = 2 x - 7g(x)=2x−7 , find g(f(x))g ( f ( x ) )g(f(x)) .