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ACT Math: Function Transformations

The ACT Math test will always include at least a few problems involving functions.  Many of these questions will be in the final one-third of the test where the more difficult problems appear.  One of the function topics you’ll want to be familiar with is function transformations, which are the explicit rules for how a change in a function’s equation affects its graph.  Those changes are summarized in the table below:

Transformation Change in the Graph of f(x)
f(x + a) Moves the graph "a" units left
f(x - a) Moves the graph "a" units right
f(x) + a Moves the graph "a" unit up
f(x) - a Moves the graph "a" units down
a·f(x) Stretches the graph vertically by a factor of "a"
-f(x) Reflects the graph across the x-axis

Here are some problems involving transformation that are similar to those you could see on the ACT Math test.  Give them a try.  The solutions appear at the bottom of this post.

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