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Chapter 3: Problem 20

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 table of values for the function \(f(x)=6^{x}\) are: (-2, 0.0278), (-1, 0.1667), (0, 1), (1, 6), (2, 36). After drawing the graph, it displays an exponential growth pattern.

Step by step solution

01

Create a table of values

Let's choose values for x and substitute each into the function to find the corresponding y-values. For example, when x=-2, \(f(x) = 6^{-2} = 0.0278\). When x=-1, \(f(x) = 6^{-1} = 0.1667\). When x=0, \(f(x) = 6^{0} = 1\). When x=1, \(f(x) = 6^{1} = 6\). When x=2, \(f(x) = 6^{2} = 36\). That gives us the following table of values: (x, y): (-2, 0.0278), (-1, 0.1667), (0, 1), (1, 6), (2, 36).
02

Sketch the graph

Now, plot the pairs of (x, y) values from the table on the graph, and draw a curve that passes through these points. The graph shall start at (0,1) and rise rapidly as x increases. Note how the graph of the function becomes almost flat and very close to the x-axis as x becomes negative. This illustrates the exponential growth pattern.

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