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Chapter 3: Problem 32

Use a graphing utility to graph the exponential function. $$y=3^{-|x|}$$

Short Answer

Expert verified
The graph of the function \(y = 3^{-|x|}\) is a declining curve that is symmetric with respect to y-axis.

Step by step solution

01

Recognize the Function

Identify that the given function \(y = 3^{-|x|}\) is an exponential function, where the base is 3 and the exponent is -|x|.
02

Understand the Role of Absolute Value

Recognize that absolute value is used in parity functions. The absolute value of x causes the graph to mirror along the y-axis. This is because for any x in the domain, there is -x where \(|x| = |-x|\). Therefore, the graph will be symmetrical with respect to the y-axis.
03

Use a Graphing Utility

Input the given function into the graphing utility along with the function \(y=3^x\). Observe the plotted graph and note how the graph is symmetric around y-axis and it diminishes as x tends more and more to negative and positive infinity.

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Most popular questions from this chapter

Function \(\quad\) Value $$ g(x)=-\ln x \quad x=\frac{1}{2}$$

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$3-\ln x=0$$

Solve the equation algebraically. Round your result to three decimal places. Verify your answer using a graphing utility. $$2 x^{2} e^{2 x}+2 x e^{2 x}=0$$

You are investing \(P\) dollars at an annual interest rate of \(r,\) compounded continuously, for \(t\) years. Which of the following would result in the highest value of the investment? Explain your reasoning. (a) Double the amount you invest. (b) Double your interest rate. (c) Double the number of years.

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