Deck 4: Inverse, Exponential, and Logarithmic Functions

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

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

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

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

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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Solve for x.
​ $\log x = - 1$ ​

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.
​ $$\begin{array} { l } f ( x ) = 3 ^ { x } \\g ( x ) = 9\end{array}$$ ​ ​

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

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

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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Find the inverse function of $f ( x ) = \sqrt { 25 - x ^ { 2 } } , 0 \leq x \leq 5$ .
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Evaluate the function at the indicated value of x. Round your result to three decimal places.
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Function
Value $f ( x ) = 3 ^ { x }$ $x = - \pi$ ​

Match the graph with its exponential function.
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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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