Question 1

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.
​

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 2

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

Accepted Answer

$$f ^ { - 1 } ( x ) = \sqrt { 25 - x ^ { 2 } } , 0 \leq x \leq 5$$

Question 3

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

Accepted Answer

​

Question 4

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

Accepted Answer

The answer of Simplify the expression \(\log _ { 3...

Question 5

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

Accepted Answer

The answer of Determine whether the function has an inverse...

Question 6

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

Accepted Answer

The answer of Approximate the point of intersection of the...

Question 7

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

Accepted Answer

The answer of Select the graph of the function.
​ \(f...

Question 8

Match the graph with its exponential function.
​  ​

Accepted Answer

The answer of Match the graph with its exponential function.
​...

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.
​ $f ( x ) = \log _ { 4 } ( x )$ ​

Accepted Answer

The answer of Use the change-of-base formula to rewrite the...

Question 10

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

Accepted Answer

The answer of Use a graphing utility to construct a...

Question 11

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

Accepted Answer

The answer of Evaluate the function at the indicated value...

Question 12

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?
​

Accepted Answer

The answer of Your wage is $11.00 per hour plus...

Question 13

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

Accepted Answer

The answer of Use the functions given by \(f (...

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

The answer of Use a graphing utility to construct a...

Question 15

Solve for x.
​ $\log x = - 1$ ​

Accepted Answer

The answer of Solve for x.
​ \(\log x = -...

Exam 4: Inverse, Exponential, and Logarithmic Functions

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.

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

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. $f ( x ) = - 3$

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

Match the graph with its exponential function.

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

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

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

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?

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

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

Solve for x. $\log x = - 1$

Exam 4: Inverse, Exponential, and Logarithmic Functions

Use a graphing utility to graph the functions given by ​ y1=ln⁡(x)−ln⁡(x−4)y _ { 1 } = \ln ( x ) - \ln ( x - 4 )y1​=ln(x)−ln(x−4) ​ and ​ y2=ln⁡xx−4y _ { 2 } = \ln \frac { x } { x - 4 }y2​=lnx−4x​ ​ in the same viewing window. ​

Find the inverse function of f(x)=25−x2,0≤x≤5f ( x ) = \sqrt { 25 - x ^ { 2 } } , 0 \leq x \leq 5f(x)=25−x2​,0≤x≤5 . ​

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

Simplify the expression log⁡3(127)2\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 2 }log3​(271​)2 .

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

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

Select the graph of the function. ​ f(x)=(12)−xf ( x ) = \left( \frac { 1 } { 2 } \right) ^ { - x }f(x)=(21​)−x ​

Match the graph with its exponential function. ​ ​

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)f ( x ) = \log _ { 4 } ( x )f(x)=log4​(x) ​

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. ​ f(x)=(13)xf ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }f(x)=(31​)x ​

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

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+1.25xy = 11 + 1.25 xy=11+1.25x . Find the inverse function. What does each variable represent in the inverse function? ​

Use the functions given by f(x)=127x−5f ( x ) = \frac { 1 } { 27 } x - 5f(x)=271​x−5 and g(x)=x3g ( x ) = x ^ { 3 }g(x)=x3 to find (f∘g)−1( f \circ g ) ^ { - 1 }(f∘g)−1 . ​

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 ​

Solve for x. ​ log⁡x=−1\log x = - 1logx=−1 ​

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.

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

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. $f ( x ) = - 3$

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

Match the graph with its exponential function.

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

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

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

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?

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

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

Solve for x. $\log x = - 1$