3.1 Functions and Function Notation

What is the difference between a relation and a function?

A relation is a set of ordered pairs; a function is a special kind of relation in which no two ordered pairs have the same first coordinate.

Let f(x) = 9x − 29. What ordered pair in f corresponds to the equation f(x) = 7? Recall y = f(x).

(x,y) = (4,7)

Determine whether the relation represents y as a function of x. 6x + 5y = 30

This relation is a function because there is only one value of y for each input x.

Determine whether the relation represents y as a function of x. x^2 + y^2 = 81

This relation is not a function because there are values of x that correspond to more than one value of y.

Find f(a + 7). f(x) = x2 + 3

f(a + 7) = a^2+14a+52

Given the following function, find h(4). h(t) = t2 − t + 9

h(4) = 21