1. (a) If y is increased by t, find an expression for 3y2+2y.
(b) Given f(x) = -2x2+3x, find f(x+h).
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)).
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.