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Chapter 3: Problem 19

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=6^{-x}$$

Short Answer

Expert verified
The plot of \(f(x)=6^{-x}\) is a decreasing curve, starting from a high value for negative x-values and decreasing to zero as x increases, never touching the x-axis. It represents the function \(f(x)=1/6^{x}\). Equivalent table values for example are: for \(x = -2, -1, 0, 1, 2\), the \(f(x)\) values will be: 36, 6, 1, 1/6, 1/36.

Step by step solution

01

Understanding the function

The function given is \(f(x) = 6^{-x}\). Negative exponent implies that the function \( f(x) \) is a reciprocal of \( 6^{x} \). Therefore, \(f(x) = 1 / 6^{x}\).
02

Constructing the table of values

Now, construct a table of values. Choose some values for \(x\), both negative and positive, and calculate the corresponding \(f(x)\) for each \(x\) value using the function \(f(x) = 1 / 6^{x}\). For example, with \(x = -2, -1, 0, 1, 2\), the \(f(x)\) values will be: 36, 6, 1, 1/6, 1/36, respectively.
03

Plotting the graph

The x-values are plotted on the horizontal axis and the corresponding \(f(x)\) values on the vertical axis. The points are then connected to form the graph. The graph is a decreasing curve, approaching zero as \(x\) tends towards positive infinity, and approaching positive infinity as \(x\) tends towards negative infinity.

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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. $$2 x \ln \left(\frac{1}{x}\right)-x=0$$

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