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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 \(g(x) = 1 + e^{-x}\) is a horizontal curve, similar to an exponential decay function, which is slightly shifted upwards due to the '+1' in the function. As \(x\) becomes larger, the function's value tends towards 1.

Step by step solution

01

Understanding the Function

The function \(g(x) = 1+ e^{-x}\) is a horizontal shift of the usual exponential decay function \(g(x)=e^{-x}\). The '+1' in the function shifts the curve upwards by 1 unit.
02

Entering the Function into Graphing Utility

Type the function into the graphing utility or calculator exactly as follows: 'y = 1 + e^ - x'. Once entered, hit the 'GRAPH' button or an equivalent depending on your specific calculator or online tool, allowing the tool to produce the graph.
03

Interpreting the Graph

Observe the produced graph. You will notice that it is a horizontal curve that is shifted one unit upwards. As x goes to positive infinity, the function's value approaches 1 (this is the horizontal asymptote at y=1). As x goes to negative infinity, the function grows without bound.

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Most popular questions from this chapter

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

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Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$10-4 \ln (x-2)=0$$

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