Question 1

Graph the function using translations.​ $$f ( x ) = 4 ^ { x + 1 } + 1$$ ​

Accepted Answer

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

Question 2

Determine whether the statement is true or false.Justify your answer. ​
The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$ ​

Accepted Answer

A) False.As $x \rightarrow 5 , f ( x ) \rightarrow 5$ but never reaches 5. 
B) True.As $x \rightarrow - 5 , f ( x ) \rightarrow - 5$ but never reaches -5. 
A) False.As $x \rightarrow 5 , f ( x ) \rightarrow 5$ but never reaches 5. 
B) True.As $x \rightarrow - 5 , f ( x ) \rightarrow - 5$ but never reaches -5.

Question 3

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 4 ^ { x }$ $x = - \pi$ ​

Accepted Answer

A)  $1.513$ 
B)  $0.013$ 
C)  $0.513$ 
D) ​ $0.121$ 
E)  $2.0129$ 
A)  $1.513$ 
B)  $0.013$ 
C)  $0.513$ 
D) ​ $0.121$ 
E)  $2.0129$

Question 4

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 2000 \left( 2 ^ { x } \right)$ $x = - 1.1$ ​

Accepted Answer

A)  $933.033$ 
B)  $102.718$ 
C)  $- 933.033$ 
D)  $1033.033$ 
E)  $- 102.718$ 
A)  $933.033$ 
B)  $102.718$ 
C)  $- 933.033$ 
D)  $1033.033$ 
E)  $- 102.718$

Question 5

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​​
Function
Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$ ​

Accepted Answer

A)  $846.800$ 
B)  $1046.800$ 
C)  $1246.800$ 
D)  $946.800$ 
E)  $1146.800$ 
A)  $846.800$ 
B)  $1046.800$ 
C)  $1246.800$ 
D)  $946.800$ 
E)  $1146.800$

Question 6

Match the graph with its exponential function.​   ​

Accepted Answer

A)  $y = 3 x$ 
B)  $y = - 3 ^ { - x }$ 
C)  $y = - 3 ^ { x }$ 
D)  $y = 3 ^ { x }$ 
E)  $y = 3 ^ { - x }$ 
A)  $y = 3 x$ 
B)  $y = - 3 ^ { - x }$ 
C)  $y = - 3 ^ { x }$ 
D)  $y = 3 ^ { x }$ 
E)  $y = 3 ^ { - x }$

Question 7

Evaluate the function $$f ( x ) = 1.3 ^ { x }$$ at $x = 3.6$ .Round to 3 decimal places.

Accepted Answer

A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690 
A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690

Question 8

Let Q represent a mass of radioactive plutonium $\left( { } ^ { 239 } \mathrm { Pu } \right)$ (in grams),whose half life is 24,100 years.The quantity of plutonium present after t years is $Q = 16 \left( \frac { 1 } { 2 } \right) ^ { t / 24,100 }$ .Determine the quantity present after 67,000 years.Round your answer to one decimal place. ​

Accepted Answer

A) 4.3 g 
B) 3.3 g 
C) 5.3 g 
D) 2.3 g 
E) 6.3 g 
A) 4.3 g 
B) 3.3 g 
C) 5.3 g 
D) 2.3 g 
E) 6.3 g

Question 9

Select the graph of the function.​ $$f ( x ) = e ^ { 4 x }$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 10

Identify the graph of the function.​ $$f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$$

Accepted Answer

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

Question 11

Identify the graph of the function.​ $f ( x ) = 3 - 5 ^ { x }$ ​

Accepted Answer

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

Question 12

Graph the function.​ $$f ( x ) = 3 ^ { x }$$ ​

Accepted Answer

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

Question 13

Use the One-to-One Property to solve the equation for x.​ $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$ ​

Accepted Answer

A)  $x = 3$ 
B)  $x = - 2$ 
C)  $x = 2$ 
D)  $x = - 3$ 
E)  $x = 4$ 
A)  $x = 3$ 
B)  $x = - 2$ 
C)  $x = 2$ 
D)  $x = - 3$ 
E)  $x = 4$

Question 14

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.​ $$f ( x ) = 6 e ^ { x - 2 } + 7$$ ​

Accepted Answer

A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & - & - \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & - & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & - & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
A)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & - & - & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & - & - \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & - & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & - & & & \
f ( x ) & 7.110 & 7.299 & 7.812 & 9.207 & 13 \
\hline
\end{array}$$

Question 15

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. ​​
Function
Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$ ​

Accepted Answer

A)  $2.504 \times 10 ^ { 2 }$ 
B)  $4.368 \times 10 ^ { 4 }$ 
C)  $3.048 \times 10 ^ { 36 }$ 
D)  $1.183 \times 10 ^ { 2 }$ 
E)  $2.777 \times 10 ^ { 21 }$ 
A)  $2.504 \times 10 ^ { 2 }$ 
B)  $4.368 \times 10 ^ { 4 }$ 
C)  $3.048 \times 10 ^ { 36 }$ 
D)  $1.183 \times 10 ^ { 2 }$ 
E)  $2.777 \times 10 ^ { 21 }$

Question 16

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​
Function
Value $f ( x ) = 0.7 ^ { x }$ $$x = 1.7$$ ​

Accepted Answer

A)  $$- 0.545$$ 
B)  $1.7$ 
C)  $0.545$ 
D)  $0.7$ 
E)  $- 1.7$ 
A)  $$- 0.545$$ 
B)  $1.7$ 
C)  $0.545$ 
D)  $0.7$ 
E)  $- 1.7$

Question 17

Select the graph of the function.​ $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { - x }$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 18

Select the graph of the exponential function. ​​ $$f ( x ) = 2 ^ { - x ^ { 2 } }$$ ​

Accepted Answer

A) ​   ​ 
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   ​ 
B) ​   
C) ​   
D) ​   
E) ​

Question 19

Evaluate the function at the indicated value of x.Round the result to three decimal places. ​
Function
Value $h ( x ) = 4000 e ^ { 0.06 x }$ $x = 5$

Accepted Answer

A)  $5599.435$ 
B)  $5499.435$ 
C)  $5449.435$ 
D)  $5749.435$ 
E)  $5399.435$ 
A)  $5599.435$ 
B)  $5499.435$ 
C)  $5449.435$ 
D)  $5749.435$ 
E)  $5399.435$

Question 20

Sketch the graph of the function.​ $f ( x ) = 2 - 2 ^ { x }$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Exam 18: Exponential Functions and Their Graphs

Graph the function using translations.​ f(x)=4x+1+1f ( x ) = 4 ^ { x + 1 } + 1f(x)=4x+1+1 ​

Determine whether the statement is true or false.Justify your answer. ​ The line y=−5y = - 5y=−5 is an asymptote for the graph of f(x)=10x−5f ( x ) = 10 ^ { x } - 5f(x)=10x−5 ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value f(x)=4xf ( x ) = 4 ^ { x }f(x)=4x x=−πx = - \pix=−π ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value f(x)=2000(2x)f ( x ) = 2000 \left( 2 ^ { x } \right)f(x)=2000(2x) x=−1.1x = - 1.1x=−1.1 ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​​ Function Value h(x)=400e0.05xh ( x ) = 400 e ^ { 0.05 x }h(x)=400e0.05x x=15x = 15x=15 ​

Match the graph with its exponential function.​ ​

Evaluate the function f(x)=1.3xf ( x ) = 1.3 ^ { x }f(x)=1.3x at x=3.6x = 3.6x=3.6 .Round to 3 decimal places.

Select the graph of the function.​ f(x)=e4xf ( x ) = e ^ { 4 x }f(x)=e4x ​

Identify the graph of the function.​ f(x)=(17)xf ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }f(x)=(71​)x

Identify the graph of the function.​ f(x)=3−5xf ( x ) = 3 - 5 ^ { x }f(x)=3−5x ​

Graph the function.​ f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x ​

Use the One-to-One Property to solve the equation for x.​ (12)x=4\left( \frac { 1 } { 2 } \right) ^ { x } = 4(21​)x=4 ​

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places.​ f(x)=6ex−2+7f ( x ) = 6 e ^ { x - 2 } + 7f(x)=6ex−2+7 ​

Evaluate the function at the indicated value of xxx .Round your result to three decimal places. ​​ Function Value f(x)=200(1.3)12xf ( x ) = 200 ( 1.3 ) ^ { 12 x }f(x)=200(1.3)12x x=14x = 14x=14 ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value f(x)=0.7xf ( x ) = 0.7 ^ { x }f(x)=0.7x x=1.7x = 1.7x=1.7 ​

Select the graph of the function.​ f(x)=(15)−xf ( x ) = \left( \frac { 1 } { 5 } \right) ^ { - x }f(x)=(51​)−x ​

Select the graph of the exponential function. ​​ f(x)=2−x2f ( x ) = 2 ^ { - x ^ { 2 } }f(x)=2−x2 ​

Evaluate the function at the indicated value of x.Round the result to three decimal places. ​ Function Value h(x)=4000e0.06xh ( x ) = 4000 e ^ { 0.06 x }h(x)=4000e0.06x x=5x = 5x=5

Sketch the graph of the function.​ f(x)=2−2xf ( x ) = 2 - 2 ^ { x }f(x)=2−2x ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Graph the function using translations. $f ( x ) = 4 ^ { x + 1 } + 1$

Determine whether the statement is true or false.Justify your answer. The line $y = - 5$ is an asymptote for the graph of $f ( x ) = 10 ^ { x } - 5$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 4 ^ { x }$ $x = - \pi$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 2000 \left( 2 ^ { x } \right)$ $x = - 1.1$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $h ( x ) = 400 e ^ { 0.05 x }$ $x = 15$

Match the graph with its exponential function.

Evaluate the function $f ( x ) = 1.3 ^ { x }$ at $x = 3.6$ .Round to 3 decimal places.

Select the graph of the function. $f ( x ) = e ^ { 4 x }$

Identify the graph of the function. $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$

Identify the graph of the function. $f ( x ) = 3 - 5 ^ { x }$

Graph the function. $f ( x ) = 3 ^ { x }$

Use the One-to-One Property to solve the equation for x. $\left( \frac { 1 } { 2 } \right) ^ { x } = 4$

Use a graphing utility to construct a table of values for the function.Round your answer to three decimal places. $f ( x ) = 6 e ^ { x - 2 } + 7$

Evaluate the function at the indicated value of $x$ .Round your result to three decimal places. Function Value $f ( x ) = 200 ( 1.3 ) ^ { 12 x }$ $x = 14$

Evaluate the function at the indicated value of x.Round your result to three decimal places. Function Value $f ( x ) = 0.7 ^ { x }$ $x = 1.7$

Select the graph of the function. $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { - x }$

Select the graph of the exponential function. $f ( x ) = 2 ^ { - x ^ { 2 } }$

Evaluate the function at the indicated value of x.Round the result to three decimal places. Function Value $h ( x ) = 4000 e ^ { 0.06 x }$ $x = 5$

Sketch the graph of the function. $f ( x ) = 2 - 2 ^ { x }$