**Comparing
graphs**

Graph each of these function equations.

(a) y = (2/5) x

(b) y = (2/5) x^2

(c) y = (2/5) x^3

(d) y = -(2/5) x

(e) y = -(2/5)x^2

(f) y = -(2/5)x^3

Then write down as many properties as possible that two or more of these functions have in common. (Becker and Shimada)

**Approaches**

They all have a factor of 2/5 (or –2/5).

What if they had another factor?

The ones with x make straight lines.

Why?

The ones with x^2 make curves.

Why? Do you know what that shape is called?

The ones with –2/5 are backward from those with 2/5.

What do you mean by "backward"? Do you know what a reflection is? Do opposite coefficients always produce reflections through the horizontal axis? Are there reflections through the vertical axis?

**Your
experience**

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

*Last updated 30 November, 2004*