Deck 4: Inverse, Exponential, and Logarithmic Functions

Question 1

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places.
​ $$f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$$ ​

Answer 1

$$\begin{array} { | c | c | c | c | c | c | } \hline x & - 2 & - 1 & 0 & 1 & 2 \\\hline f ( x ) & 9.00 & 3.00 & 1.00 & 0.33 & 0.11 \\\hline\end{array}$$

Question 2

Select the graph of the function.
​ $f ( x ) = \log ( x + 4 )$ ​

Answer 2

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Question 3

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 2 }$ .

Answer 3

-6

Question 4

Determine whether the function has an inverse function. If it does, find the inverse function.
​ $f ( x ) = - 3$ ​

Question 5

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

Question 6

Your wage is $11.00 per hour plus $1.25 for each unit produced per hour. So, your hourly wage in terms of the number of units produced x is $y = 11 + 1.25 x$ . Find the inverse function. What does each variable represent in the inverse function?
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Question 7

Solve for x.
​ $\log x = - 1$ ​

Question 8

Approximate the point of intersection of the graphs of f and g. Then solve the equation $f ( x ) = g ( x )$ algebraically to verify your approximation.
​ $$\begin{array} { l } f ( x ) = 3 ^ { x } \\g ( x ) = 9\end{array}$$ ​ ​

Question 9

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms. Then use a
graphing utility to graph the ratio.
​ $f ( x ) = \log _ { 4 } ( x )$ ​

Question 10

Select the graph of the function.
​ $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { - x }$ ​

Question 11

Use the functions given by $f ( x ) = \frac { 1 } { 27 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .
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Question 12

Find the inverse function of $f ( x ) = \sqrt { 25 - x ^ { 2 } } , 0 \leq x \leq 5$ .
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Question 13

Evaluate the function at the indicated value of x. Round your result to three decimal places.
​
Function
Value $f ( x ) = 3 ^ { x }$ $x = - \pi$ ​

Question 14

Match the graph with its exponential function.
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Question 15

Use a graphing utility to graph the functions given by
​ $y _ { 1 } = \ln ( x ) - \ln ( x - 4 )$ ​
and
​ $y _ { 2 } = \ln \frac { x } { x - 4 }$ ​
in the same viewing window.
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