Question 1

Express the following logarithm as specified.
-$\ln 1225$ in terms of $\ln 5$ and $\ln 7$

Accepted Answer

A)  $2 \ln 5 + 2 \ln 7$ 
B)  $2 \ln 5 - 2 \ln 7$ 
C)  $4 \ln 5$ 
D)  $- 2 \ln 5 - 2 \ln 7$ 
A)  $2 \ln 5 + 2 \ln 7$ 
B)  $2 \ln 5 - 2 \ln 7$ 
C)  $4 \ln 5$ 
D)  $- 2 \ln 5 - 2 \ln 7$

Question 2

Find the exact function value.
-$\operatorname { arccsc } ( - 2 )$

Accepted Answer

A)  $- \frac { \pi } { 6 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { \pi } { 3 }$ 
A)  $- \frac { \pi } { 6 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { \pi } { 3 }$

Question 3

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

Accepted Answer

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

Question 4

Express the given quantity in terms of sin x or cos x.
-$\cos ( 2 \pi - x )$

Accepted Answer

A)  $\cos x + \sin x$ 
B)  $- \cos x$ 
C)  $\cos x - \sin x$ 
D)  $\cos x$ 
A)  $\cos x + \sin x$ 
B)  $- \cos x$ 
C)  $\cos x - \sin x$ 
D)  $\cos x$

Question 5

Determine if the function is even, odd, or neither.
-$$g ( x ) = \left| 5 x ^ { 7 } \right|$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 6

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y=-2 \sqrt{x}$

Accepted Answer

A)  Decreasing $- \infty < x < \infty$
  
B)  Increasing $0 \leq x < \infty$
  
C)  Decreasing $0 \leq x < \infty$
  
D)  Increasing $0 \leq x < \infty$
  
A)  Decreasing $- \infty < x < \infty$
  
B)  Increasing $0 \leq x < \infty$
  
C)  Decreasing $0 \leq x < \infty$
  
D)  Increasing $0 \leq x < \infty$

Question 7

Graph the function.
-$$\mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }$$

Accepted Answer

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

Question 8

Find the domain and range for the indicated function.
-$f ( x ) = 6 , \quad g ( x ) = 6 + \sqrt { x }$
$\mathrm { g } / \mathrm { f }$

Accepted Answer

A)  D: $x \geq 0$
R: $y \geq 1$ 
B)  D: $x \geq - 6$
$R : y \geq 0$ 
C)  D: $x \geq 0$
$R : y \leq 6$ 
D)  D: $x \geq 0$
R: $y \leq 1$ 
A)  D: $x \geq 0$
R: $y \geq 1$ 
B)  D: $x \geq - 6$
$R : y \geq 0$ 
C)  D: $x \geq 0$
$R : y \leq 6$ 
D)  D: $x \geq 0$
R: $y \leq 1$

Question 9

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$7 e ^ { 4 x + 4 } = 5$$

Accepted Answer

A)  -0.014 
B)  -1.986 
C)  -2.154 
D)  -1.084 
A)  -0.014 
B)  -1.986 
C)  -2.154 
D)  -1.084

Question 10

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 11

Graph the function.
-$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2$

Accepted Answer

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

Question 12

Solve the problem.
-The decay of 608 mg of an isotope is given by A $$A ( t ) = 608 e ^ { - 0.019 t }$$ , where t is time in years. Find the amount left after 50 years.

Accepted Answer

A)  235 mg 
B)  231 mg 
C)  597 mg 
D)  118 mg 
A)  235 mg 
B)  231 mg 
C)  597 mg 
D)  118 mg

Question 13

Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\sin \left( \frac { 5 \pi } { 3 } \right)$

Accepted Answer

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

Question 14

Solve the problem.
-Boyle's Law says that volume $\mathrm { V }$ of a gas at constant temperature increases whenever the pressure $\mathrm { P }$ decreases, so that $\mathrm { V }$ and $\mathrm { P }$ are inversely proportional. If $\mathrm { P } = 14.5 \mathrm { lbs } / \mathrm { in } ^ { 2 }$ when $\mathrm { V } = 1100$ in 3 , then what is $\mathrm { V }$ when $\mathrm { P } = 24 \mathrm { lbs } /$ in $^ { 2 }$ ?

Accepted Answer

A)  $\frac { 87 } { 275 }$ in $^ { 3 }$ 
B)  $\frac { 7975 } { 12 } \mathrm { in } ^ { 3 }$ 
C)  $\frac { 52800 } { 29 } \mathrm { in } ^ { 3 }$ 
D)  $\frac { 275 } { 87 } \mathrm { in } ^ { 3 }$ 
A)  $\frac { 87 } { 275 }$ in $^ { 3 }$ 
B)  $\frac { 7975 } { 12 } \mathrm { in } ^ { 3 }$ 
C)  $\frac { 52800 } { 29 } \mathrm { in } ^ { 3 }$ 
D)  $\frac { 275 } { 87 } \mathrm { in } ^ { 3 }$

Question 15

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

Accepted Answer

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

Question 16

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

Accepted Answer

A)  $1475.96 
B)  $973.82 
C)  $1210.68 
D)  $2210.68 
A)  $1475.96 
B)  $973.82 
C)  $1210.68 
D)  $2210.68

Question 17

Solve the problem.
-In the formula A $$\mathrm { A } = \mathrm { Ie }^{ { kt }}$$ A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope has a
Half-life of approximately 1450 years. How many years would be required for a given amount of this isotope to
Decay to 60% of that amount?

Accepted Answer

A)  1069 yr 
B)  580 yr 
C)  1009 yr 
D)  1917 yr 
A)  1069 yr 
B)  580 yr 
C)  1009 yr 
D)  1917 yr

Question 18

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\sin x = - \frac { 1 } { 5 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Accepted Answer

A)  $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$ 
B)  $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$ 
C)  $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$ 
D)  $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$ 
A)  $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$ 
B)  $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = - \frac { \sqrt { 6 } } { 12 }$ 
C)  $\cos x = - \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$ 
D)  $\cos x = \frac { 2 \sqrt { 6 } } { 5 } , \tan x = \frac { \sqrt { 6 } } { 12 }$

Question 19

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 14 x ^ { 2 } + x - 18$

Accepted Answer

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

Question 20

Find the domain and range of the inverse of the given function.
-$$f ( x ) = 4.9 + 1.72 x$$

Accepted Answer

A)  Domain: $[ 4.9 , \infty )$; range: all real numbers 
B)  Domain: all real numbers; range: $( - \infty , 4.9 ]$ 
C)  Domain: all real numbers; range: $[ 4.9 , \infty )$ 
D)  Domain and range: all real numbers 
A)  Domain: $[ 4.9 , \infty )$; range: all real numbers 
B)  Domain: all real numbers; range: $( - \infty , 4.9 ]$ 
C)  Domain: all real numbers; range: $[ 4.9 , \infty )$ 
D)  Domain and range: all real numbers

Express the following logarithm as specified. - $\ln 1225$ in terms of $\ln 5$ and $\ln 7$

Find the exact function value. - $\operatorname { arccsc } ( - 2 )$

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

Express the given quantity in terms of sin x or cos x. - $\cos ( 2 \pi - x )$

Determine if the function is even, odd, or neither. - $g ( x ) = \left| 5 x ^ { 7 } \right|$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=-2 \sqrt{x}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=-2 \sqrt{x}$

Graph the function. - $\mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }$ $Graph the function. - \mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }$

Find the domain and range for the indicated function. - $f ( x ) = 6 , \quad g ( x ) = 6 + \sqrt { x }$ $\mathrm { g } / \mathrm { f }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $7 e ^ { 4 x + 4 } = 5$

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

Graph the function. - $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2$

Solve the problem. -The decay of 608 mg of an isotope is given by A $A ( t ) = 608 e ^ { - 0.019 t }$ , where t is time in years. Find the amount left after 50 years.

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\sin \left( \frac { 5 \pi } { 3 } \right)$

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

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = - \frac { 1 } { 5 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Find the domain and range of the inverse of the given function. - $f ( x ) = 4.9 + 1.72 x$

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

Express the following logarithm as specified. - ln⁡1225\ln 1225ln1225 in terms of ln⁡5\ln 5ln5 and ln⁡7\ln 7ln7

Find the exact function value. - arccsc⁡(−2)\operatorname { arccsc } ( - 2 )arccsc(−2)

Solve for the angle , where 0 2 - cos⁡2θ=14\cos ^ { 2 } \theta = \frac { 1 } { 4 }cos2θ=41​

Express the given quantity in terms of sin x or cos x. - cos⁡(2π−x)\cos ( 2 \pi - x )cos(2π−x)

Determine if the function is even, odd, or neither. - g(x)=∣5x7∣g ( x ) = \left| 5 x ^ { 7 } \right|g(x)=​5x7​

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−2xy=-2 \sqrt{x}y=−2x​

Graph the function. - y=1(x−1)2\mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }y=(x−1)21​

Find the domain and range for the indicated function. - f(x)=6,g(x)=6+xf ( x ) = 6 , \quad g ( x ) = 6 + \sqrt { x }f(x)=6,g(x)=6+x​ g/f\mathrm { g } / \mathrm { f }g/f

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 7e4x+4=57 e ^ { 4 x + 4 } = 57e4x+4=5

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

Graph the function. - f(x)=(15)x+2f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2f(x)=(51​)x+2

Solve the problem. -The decay of 608 mg of an isotope is given by A A(t)=608e−0.019tA ( t ) = 608 e ^ { - 0.019 t }A(t)=608e−0.019t , where t is time in years. Find the amount left after 50 years.

Find the exact value of the trigonometric function. Do not use a calculator or tables. - sin⁡(5π3)\sin \left( \frac { 5 \pi } { 3 } \right)sin(35π​)

Use the appropriate addition formula to find the exact value of the expression. - tan⁡(−7π12)\tan \left( - \frac { 7 \pi } { 12 } \right)tan(−127π​)

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - sin⁡x=−15,x\sin x = - \frac { 1 } { 5 } , \quad xsinx=−51​,x in [−π2,0]\left[ - \frac { \pi } { 2 } , 0 \right][−2π​,0]

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=x4−4x3+14x2+x−18f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 14 x ^ { 2 } + x - 18f(x)=x4−4x3+14x2+x−18

Find the domain and range of the inverse of the given function. - f(x)=4.9+1.72xf ( x ) = 4.9 + 1.72 xf(x)=4.9+1.72x

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

Express the following logarithm as specified. - $\ln 1225$ in terms of $\ln 5$ and $\ln 7$

Find the exact function value. - $\operatorname { arccsc } ( - 2 )$

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

Express the given quantity in terms of sin x or cos x. - $\cos ( 2 \pi - x )$

Determine if the function is even, odd, or neither. - $g ( x ) = \left| 5 x ^ { 7 } \right|$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=-2 \sqrt{x}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=-2 \sqrt{x}$

Graph the function. - $\mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }$ $Graph the function. - \mathrm { y } = \frac { 1 } { ( \mathrm { x } - 1 ) ^ { 2 } }$

Find the domain and range for the indicated function. - $f ( x ) = 6 , \quad g ( x ) = 6 + \sqrt { x }$ $\mathrm { g } / \mathrm { f }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $7 e ^ { 4 x + 4 } = 5$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } + 2$

Solve the problem. -The decay of 608 mg of an isotope is given by A $A ( t ) = 608 e ^ { - 0.019 t }$ , where t is time in years. Find the amount left after 50 years.

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\sin \left( \frac { 5 \pi } { 3 } \right)$

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

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = - \frac { 1 } { 5 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Find the domain and range of the inverse of the given function. - $f ( x ) = 4.9 + 1.72 x$