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Chapter 3: Problem 43

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=2 e^{x-2}+4$$

Short Answer

Expert verified
The graph of the function \(f(x)=2 e^{x-2}+4\) rises exponentially after the point (2,4). Before this point, it lies below the y-axis. The exact shape would depend on the table of values obtained.

Step by step solution

01

Generate the Table of Values

Using a graphing utility, plug the values of x, ranging from -2 to 2, into the function \(f(x)=2 e^{x-2}+4\). Calculate the respective y values and organize them into a table.
02

Plot the Points

Plot these points on a graph using the x-values as the horizontal ones and the y-values as the vertical ones. Be sure to label each point with its (x,y) coordinates.
03

Draw the Graph

Connect the plotted points with a smooth curve. This will give the graph of the function. It should start from below at negative x coordinates, go through the point (2,4), and rise exponentially at x values greater than 2.

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