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Chapter 3: Problem 17

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$f(x)=(0.6)^{x}$$

Short Answer

Expert verified
The graph of the function \(f(x)=(0.6)^{x}\) starts from the top left and decreases towards the x-axis as x increases. The y-values decrease in an exponential manner.

Step by step solution

01

Create a Table of Coordinates

Start by determining a list of x-values. For this exponential function, the values -2, -1, 0, 1, 2 would be a good choice. Then, compute the corresponding y-values using the function \(f(x) = (0.6)^{x}\).
02

Plot the Points on the Graph

Once the coordinates are determined, plot each point on the graph. These points should give a rough approximation of the graph shape, which in the case of the function \(f(x)=(0.6)^{x}\) will be decreasing as x increases.
03

Sketch the Graph

Connect the dots with a smooth curve. Because the function is defined for all real numbers, make sure the curve extends to the edge of the graph in both ends.
04

Confirm with a Graphing Utility

As a final step, input the function into a digital graphing tool and compare it with the hand-drawn graph to confirm it's correct. If there are discrepancies, revisit the previous steps and correct any errors.

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