Question 1

Solve the problem.
-If $f ( x ) = \frac { x - 2 } { 9 }$ and $g ( x ) = 9 x + 2$, find $g ( f ( x ) )$

Accepted Answer

A)  $9 x + 16$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $x + 4$ 
D)  $x$ 
A)  $9 x + 16$ 
B)  $- \frac { 2 } { 9 }$ 
C)  $x + 4$ 
D)  $x$

Question 2

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.
-$s=\cot 2 t$

Accepted Answer

A)  Period $\frac { \pi } { 2 }$, symmetric about the origin
  
B)  Period $\frac { \pi } { 2 }$, symmetric about the origin
  
C)  Period $\pi$, symmetric about the origin
  
D)  Period $\frac { \pi } { 2 }$, symmetric about the s-axis
  
A)  Period $\frac { \pi } { 2 }$, symmetric about the origin
  
B)  Period $\frac { \pi } { 2 }$, symmetric about the origin
  
C)  Period $\pi$, symmetric about the origin
  
D)  Period $\frac { \pi } { 2 }$, symmetric about the s-axis

Question 3

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$$2 ^ { - 4 } \cdot 2 ^ { 9 }$$

Accepted Answer

A)  $4 ^ { 36 }$ 
B)  $2 ^ { - 36 }$ 
C)  $4 ^ { 5 }$ 
D)  $2 ^ { 5 }$ 
A)  $4 ^ { 36 }$ 
B)  $2 ^ { - 36 }$ 
C)  $4 ^ { 5 }$ 
D)  $2 ^ { 5 }$

Question 4

Find the domain and range of the function.
-$F ( t ) = \frac { 4 } { \sqrt { t } }$

Accepted Answer

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

Question 5

Solve the problem.
-If $f ( x ) = \sqrt { x + 7 }$ and $g ( x ) = 8 x - 11$, find $f ( g ( x ) )$

Accepted Answer

A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x + 7 } - 11$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x + 1 }$ 
A)  $2 \sqrt { 2 x - 1 }$ 
B)  $8 \sqrt { x + 7 } - 11$ 
C)  $8 \sqrt { x - 4 }$ 
D)  $2 \sqrt { 2 x + 1 }$

Question 6

Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\csc \left( \frac { \pi } { 3 } \right)$

Accepted Answer

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

Question 7

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$5 ^ { x + 9 } = 6 ^ { x }$$

Accepted Answer

A)  -79.447 
B)  80.987 
C)  79.447 
D)  77.907 
A)  -79.447 
B)  80.987 
C)  79.447 
D)  77.907

Question 8

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Accepted Answer

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

Question 9

Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l } 
3 - x , & x \leq 2 \
1 - 4 x , & x > 2
\end{array} \right.$$

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = ( x + 1 ) ^ { 2 } + 5$ 
B)  $y = ( x - 5 ) ^ { 2 } + 1$ 
C)  $y = ( x + 1 ) ^ { 2 } - 5$ 
D)  $y = ( x - 1 ) ^ { 2 } + 5$ 
A)  $y = ( x + 1 ) ^ { 2 } + 5$ 
B)  $y = ( x - 5 ) ^ { 2 } + 1$ 
C)  $y = ( x + 1 ) ^ { 2 } - 5$ 
D)  $y = ( x - 1 ) ^ { 2 } + 5$

Question 11

Find the domain and range for the indicated function.
-$f ( x ) = 2 , \quad g ( x ) = 2 + \sqrt { x } ; \quad f / g$

Accepted Answer

A)  D: $x \geq 0$
R: $y \leq 1$ 
B)  D: $x \geq 0$
R: $y \leq 2$ 
C)  D: $x \geq - 2$
R: $\mathrm { y } \geq 0$ 
D)  D: $x \geq 0$
R: $\mathrm { y } \geq 1$ 
A)  D: $x \geq 0$
R: $y \leq 1$ 
B)  D: $x \geq 0$
R: $y \leq 2$ 
C)  D: $x \geq - 2$
R: $\mathrm { y } \geq 0$ 
D)  D: $x \geq 0$
R: $\mathrm { y } \geq 1$

Question 12

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-

Accepted Answer

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

Question 13

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\tan x = - \frac { 3 } { 4 } , \quad x$ in $\left[ \frac { \pi } { 2 } , \pi \right]$

Accepted Answer

A)  $\sin x = - \frac { 3 } { 5 } , \cos x = \frac { 4 } { 5 }$ 
B)  $\sin x = \frac { 3 } { 5 } , \cos x = \frac { 4 } { 5 }$ 
C)  $\sin x = \frac { 4 } { 5 } , \cos x = - \frac { 3 } { 5 }$ 
D)  $\sin x = \frac { 3 } { 5 } , \cos x = - \frac { 4 } { 5 }$ 
A)  $\sin x = - \frac { 3 } { 5 } , \cos x = \frac { 4 } { 5 }$ 
B)  $\sin x = \frac { 3 } { 5 } , \cos x = \frac { 4 } { 5 }$ 
C)  $\sin x = \frac { 4 } { 5 } , \cos x = - \frac { 3 } { 5 }$ 
D)  $\sin x = \frac { 3 } { 5 } , \cos x = - \frac { 4 } { 5 }$

Question 14

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. How long will it take for the population of a
Certain country to triple if its annual growth rate is 2.3%? Round to the nearest year.

Accepted Answer

A)  1 yr 
B)  21 yr 
C)  48 yr 
D)  130 yr 
A)  1 yr 
B)  21 yr 
C)  48 yr 
D)  130 yr

Question 15

Solve for t or y, as appropriate.
-$$\ln ( y - 32 ) = 5 x$$

Accepted Answer

A)  $\ln ( 5 x ) + 32$ 
B)  $5 x + 32$ 
C)  $\mathrm { e } ^ { 5 \mathrm { x } } + 32$ 
D)  $\frac { 5 x + 32 } { e }$ 
A)  $\ln ( 5 x ) + 32$ 
B)  $5 x + 32$ 
C)  $\mathrm { e } ^ { 5 \mathrm { x } } + 32$ 
D)  $\frac { 5 x + 32 } { e }$

Question 16

Solve the problem.
-The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Accepted Answer

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

Question 17

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$10 ^ { 2 / 3 } \cdot 10 ^ { 3 / 4 }$

Accepted Answer

A)  $10 ^ { 17 / 12 }$ 
B)  $100 ^ { 17 / 12 }$ 
C)  $10 ^ { 1 / 2 }$ 
D)  $100 ^ { 1 / 2 }$ 
A)  $10 ^ { 17 / 12 }$ 
B)  $100 ^ { 17 / 12 }$ 
C)  $10 ^ { 1 / 2 }$ 
D)  $100 ^ { 1 / 2 }$

Question 18

State the period of the function and graph.
-$\sin \left(x+\frac{\pi}{4}\right)+3$

Accepted Answer

A)  Period $2 \pi$
  
B) $\text { Period } 2 \pi$
  
C)  $\text { Period } 2 \pi$
  
D)  $\text { Period } 2 \pi$
  
A)  Period $2 \pi$
  
B) $\text { Period } 2 \pi$
  
C)  $\text { Period } 2 \pi$
  
D)  $\text { Period } 2 \pi$

Question 19

Use the appropriate addition formula to find the exact value of the expression.
-$\cos \left( \frac { 19 \pi } { 12 } \right)$

Accepted Answer

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

Question 20

Find the exact function value.
-$\arcsin \left( - \frac { \sqrt { 2 } } { 2 } \right)$

Accepted Answer

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

Solve the problem. -If $f ( x ) = \frac { x - 2 } { 9 }$ and $g ( x ) = 9 x + 2$ , find $g ( f ( x ) )$

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - $s=\cot 2 t$ $Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - s=\cot 2 t$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $2 ^ { - 4 } \cdot 2 ^ { 9 }$

Find the domain and range of the function. - $F ( t ) = \frac { 4 } { \sqrt { t } }$

Solve the problem. -If $f ( x ) = \sqrt { x + 7 }$ and $g ( x ) = 8 x - 11$ , find $f ( g ( x ) )$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\csc \left( \frac { \pi } { 3 } \right)$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ^ { x + 9 } = 6 ^ { x }$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 3 - x , & x \leq 2 \\1 - 4 x , & x > 2\end{array} \right.$

Solve the problem. -The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Find the domain and range for the indicated function. - $f ( x ) = 2 , \quad g ( x ) = 2 + \sqrt { x } ; \quad f / g$

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\tan x = - \frac { 3 } { 4 } , \quad x$ in $\left[ \frac { \pi } { 2 } , \pi \right]$

Solve for t or y, as appropriate. - $\ln ( y - 32 ) = 5 x$

Solve the problem. -The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $10 ^ { 2 / 3 } \cdot 10 ^ { 3 / 4 }$

State the period of the function and graph. - $\sin \left(x+\frac{\pi}{4}\right)+3$ $State the period of the function and graph. - \sin \left(x+\frac{\pi}{4}\right)+3$

Use the appropriate addition formula to find the exact value of the expression. - $\cos \left( \frac { 19 \pi } { 12 } \right)$

Find the exact function value. - $\arcsin \left( - \frac { \sqrt { 2 } } { 2 } \right)$

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

Solve the problem. -If f(x)=x−29f ( x ) = \frac { x - 2 } { 9 }f(x)=9x−2​ and g(x)=9x+2g ( x ) = 9 x + 2g(x)=9x+2 , find g(f(x))g ( f ( x ) )g(f(x))

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - s=cot⁡2ts=\cot 2 ts=cot2t

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - 2−4⋅292 ^ { - 4 } \cdot 2 ^ { 9 }2−4⋅29

Find the domain and range of the function. - F(t)=4tF ( t ) = \frac { 4 } { \sqrt { t } }F(t)=t​4​

Solve the problem. -If f(x)=x+7f ( x ) = \sqrt { x + 7 }f(x)=x+7​ and g(x)=8x−11g ( x ) = 8 x - 11g(x)=8x−11 , find f(g(x))f ( g ( x ) )f(g(x))

Find the exact value of the trigonometric function. Do not use a calculator or tables. - csc⁡(π3)\csc \left( \frac { \pi } { 3 } \right)csc(3π​)

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 5x+9=6x5 ^ { x + 9 } = 6 ^ { x }5x+9=6x

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=2x2x2−4f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }f(x)=x2−42x2​

Determine from its graph if the function is one-to-one. - f(x)={3−x,x≤21−4x,x>2f ( x ) = \left\{ \begin{array} { l l } 3 - x , & x \leq 2 \\1 - 4 x , & x > 2\end{array} \right.f(x)={3−x,1−4x,​x≤2x>2​

Solve the problem. -The accompanying figure shows the graph of y=x2y = x ^ { 2 }y=x2 shifted to a new position. Write the equation for the new graph.

Find the domain and range for the indicated function. - f(x)=2,g(x)=2+x;f/gf ( x ) = 2 , \quad g ( x ) = 2 + \sqrt { x } ; \quad f / gf(x)=2,g(x)=2+x​;f/g

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - tan⁡x=−34,x\tan x = - \frac { 3 } { 4 } , \quad xtanx=−43​,x in [π2,π]\left[ \frac { \pi } { 2 } , \pi \right][2π​,π]

Solve for t or y, as appropriate. - ln⁡(y−32)=5x\ln ( y - 32 ) = 5 xln(y−32)=5x

Solve the problem. -The accompanying figure shows the graph of y=x2y = x ^ { 2 }y=x2 shifted to a new position. Write the equation for the new graph.

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - 102/3⋅103/410 ^ { 2 / 3 } \cdot 10 ^ { 3 / 4 }102/3⋅103/4

State the period of the function and graph. - sin⁡(x+π4)+3\sin \left(x+\frac{\pi}{4}\right)+3sin(x+4π​)+3

Use the appropriate addition formula to find the exact value of the expression. - cos⁡(19π12)\cos \left( \frac { 19 \pi } { 12 } \right)cos(1219π​)

Find the exact function value. - arcsin⁡(−22)\arcsin \left( - \frac { \sqrt { 2 } } { 2 } \right)arcsin(−22​​)

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

Solve the problem. -If $f ( x ) = \frac { x - 2 } { 9 }$ and $g ( x ) = 9 x + 2$ , find $g ( f ( x ) )$

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - $s=\cot 2 t$ $Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - s=\cot 2 t$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $2 ^ { - 4 } \cdot 2 ^ { 9 }$

Find the domain and range of the function. - $F ( t ) = \frac { 4 } { \sqrt { t } }$

Solve the problem. -If $f ( x ) = \sqrt { x + 7 }$ and $g ( x ) = 8 x - 11$ , find $f ( g ( x ) )$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\csc \left( \frac { \pi } { 3 } \right)$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ^ { x + 9 } = 6 ^ { x }$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 3 - x , & x \leq 2 \\1 - 4 x , & x > 2\end{array} \right.$

Solve the problem. -The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Find the domain and range for the indicated function. - $f ( x ) = 2 , \quad g ( x ) = 2 + \sqrt { x } ; \quad f / g$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\tan x = - \frac { 3 } { 4 } , \quad x$ in $\left[ \frac { \pi } { 2 } , \pi \right]$

Solve for t or y, as appropriate. - $\ln ( y - 32 ) = 5 x$

Solve the problem. -The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $10 ^ { 2 / 3 } \cdot 10 ^ { 3 / 4 }$

State the period of the function and graph. - $\sin \left(x+\frac{\pi}{4}\right)+3$ $State the period of the function and graph. - \sin \left(x+\frac{\pi}{4}\right)+3$

Use the appropriate addition formula to find the exact value of the expression. - $\cos \left( \frac { 19 \pi } { 12 } \right)$

Find the exact function value. - $\arcsin \left( - \frac { \sqrt { 2 } } { 2 } \right)$