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Chapter 3: Problem 49

Use a graphing utility to graph the exponential function. $$g(x)=1+e^{-x}$$

Short Answer

Expert verified
The graph of the function \(g(x)=1+e^{-x}\) starts at the point (0,2) and approaches the line \(y = 1\) as \(x\) becomes larger. The function is decreasing and convex on the interval from \(-\inf\) to \(+\inf\).

Step by step solution

01

Set up the formula

As per the exercise, the function to graph is \(g(x)=1+e^{-x}\). This is an exponential function, where \(e\) is the base of the Natural Logarithm, approximately equal to 2.71828.
02

Use a graphing utility

Utilize a graphing utility tool. It could be a physical graphing calculator or an online tool. Make sure to input the formula exactly as \(g(x)=1+e^{-x}\).
03

Graph and analyze the function

Upon inputting the function into the tool, it will display a graph. This graph starts at the point (0,2) and approaches the line \(y = 1\) as \(x\) becomes larger and larger. The function is decreasing and convex on the interval from \(-\inf\) to \(+\inf\).

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Most popular questions from this chapter

Function \(\quad\) Value $$ f(x)=\ln x \quad x=18.42$$

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

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