Moving graphs

What this chapter teaches

Four ways to move a graph y = f(x). A number added outside, f(x) + a, slides it up. A number added inside, f(x + a), slides it left by a, which surprises most people. A minus outside, −f(x), turns it over in the x axis. A minus inside, f(−x), turns it over in the y axis.

Three questions to ask

There is no one right wording. Listen for the idea.

1. Which way does y = f(x + 3) move the graph, and how do you check it using the lowest point?
2. What is the difference between y = f(x) + 3 and y = f(x + 3)?
3. Which rule turns a graph upside down, and which turns it left to right?

After the chapter, the learner can

• Sketch y = f(x) + a and y = f(x + a)
• Sketch y = −f(x) and y = f(−x)