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Chapter 3: Problem 18

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=\left(\frac{1}{2}\right)^{-x}$$

Short Answer

Expert verified
The table of values are constructed, and then these values are used to draw the graph of the function. It results in an exponential growth curve due to the negative exponent, contrary to the usual exponential decay seen with positive exponents in a function of \(f(x)=(\frac{1}{2})^{x}\).

Step by step solution

01

Set up the table

To create the table of values, select several values for x. This will create a range of x-values. Try to include negative, zero, and positive values for x to capture the behavior of the graph across the entire domain of the function.
02

Calculate the function values

For each selected x-value, calculate the corresponding function value \(f(x)=(\frac{1}{2})^{-x}\). Remember that (-x) in the exponent basically means that you take the reciprocal for positive x values. So, for example, for x=2 the value of \(f(x)\) would be \((\frac{1}{2})^{-2}= 4\).
03

Plot the points and draw the graph

Plot the points (x, f(x)) on the co-ordinate plane from the table of values. Then draw a smooth curve that fits the plotted points. The graph should clearly display the exponential decay of the function.

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