Cubic, reciprocal and circle graphs

What this chapter teaches

Three new graph shapes. y = x³ is an S through the origin. y = 1/x has two branches that approach the axes without touching them. x² + y² = r² is a circle with radius r, centre at the origin. A table of values and a few key points tell the shapes apart.

Three questions to ask

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

1. Why does y = 1/x have no point on the y axis?
2. What is the radius of the circle x² + y² = 49, and how do you know?
3. How can you tell y = x³ from y = x² by looking at the graph?

After the chapter, the learner can

• Sketch y = x³ and y = 1/x
• Sketch the circle x² + y² = 25
• Match an equation to the shape of its graph