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Chapter 3: Problem 31

Use a graphing utility to graph the exponential function. $$y=2^{-x^{2}}$$

Short Answer

Expert verified
To graph the function \(y = 2^{-x^{2}}\), input it into a graphing utility and plot the graph. It should start close to y = 1 for x = 0 and approach 0 as x moves away from 0 in either direction due to the negative squared exponent.

Step by step solution

01

Input the function

Open the graphing utility and input the function \(y = 2^{-x^{2}}\) into the function entry field. Make sure to correctly enter the function, paying attention to the negative exponent.
02

Graph the function

Once the function is correctly entered, hit the 'Graph' button or equivalent command to generate the graph. The graph should automatically adjust to fit the function.
03

Analyze the graph

Identify key features of the function on the graph. It should start close to y = 1 for x values close to 0 and rapidly decrease as x moves further from 0. This is because any number (except 0) to the power of -x^2, where x is not 0, will approach 0. For negative x values, the function acts the same because (-x)^2 = x^2.

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Most popular questions from this chapter

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

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$h(x)=\ln (x+5)$$

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

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln (x+5)=\ln (x-1)-\ln (x+1)$$

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