Assessment Problem:

1. (a) If y is increased by t, find an expression for 3y2+2y.

(b) Given f(x) = -2x2+3x, find f(x+h).

Common Responses:

For 1., students typically add t to the overall output (3y2+2y+t) or add t to each occurrence of y (3(y2+t) + 2(y+t)).

Mathematical Issues:

Students struggle with function notation. These exercises can help teachers quickly see whether their students correctly interpret and use function notation. 1(a) and 1(b) are essentially the same problem except that one uses function notation and one does not.

Domain:

Patterns & Functions

Theme:

Function notation and transformation

Common Core Standards:

7.EE: Expressions and Equations

F.BF.3

Research References:

Coady, C., & Pegg, J. (1994). Tertiary students' understanding of second order relationships in function notation. Paper presented at the 17th Annual Mathematics Education Research Group of Australasia Conference.