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.