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)


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

What if they had another factor?

The ones with x make straight lines.


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