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Chapter 3: Problem 71

Use a graphing utility to graph the function. Be sure to use an appropriate viewing window. \(f(x)=\ln x+8\)

Short Answer

Expert verified
The graph of the function \(f(x)=\ln x+8\) rises slowly and indefinitely to the right, crossing the y-axis at \(y=8\).

Step by step solution

01

Identify the range of the function

For the function \(f(x)=\ln x+8\), the range would be from -鈭� to +鈭� since \(\ln x\) can take any possible real value and no restrictions are made by +8.
02

Choose an appropriate viewing window for the x-values

The function \(f(x)=\ln x+8\) is only defined for values of \(x>0\). It is advisable to set the lower limit of the viewing window close to zero. For example, you could make the x-values range from 0.1 to 10.
03

Choose an appropriate viewing window for the y-values

Based on the range of the function from Step 1, the y-values could technically span all real numbers. However, to get a focused view of the graph near where it crosses the y-axis, you might set the y-values to range from -2 to 10.
04

Graph the function

After setting the appropriate viewing window, you can then plot the function \(f(x)=\ln x+8\) using the graphing utility. You should see a graph that rises slowly and indefinitely to the right.

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Most popular questions from this chapter

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$6 e^{1-x}=25$$

Use a graphing utility to graph the function. Be sure to use an appropriate viewing window. \(f(x)=\ln (x-1)\)

Solve the equation algebraically. Round your result to three decimal places. Verify your answer using a graphing utility. $$\frac{1-\ln x}{x^{2}}=0$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2} x+\log _{2}(x+2)=\log _{2}(x+6)$$

Writing Use your school's library, the Internet, or some other reference source to write a paper describing John Napier's work with logarithms.
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