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Example 20 from Algebra and Trigonometry, 3.5 Transformation of Functions
Finding a Triple Transformation of a Graph
Use the graph of in Figure 27 to sketch a graph of
Figure
27
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
To simplify, let’s start by factoring out the inside of the function.
By factoring the inside, we can first horizontally stretch by 2, as indicated by the on the inside of the function. Remember that twice the size of 0 is still 0, so the point (0,2) remains at (0,2) while the point (2,0) will stretch to (4,0). See Figure 28.
Figure 28Next, we horizontally shift left by 2 units, as indicated by See Figure 29.
Figure 29Last, we vertically shift down by 3 to complete our sketch, as indicated by the on the outside of the function. See Figure 30.
Figure 30
How did it go?