cmc south kathleen strange understanding functions (c) 2013 kathleen strange

(c) 2013 Kathleen Strange

CMC South Kathleen Strange

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

This is a function. This is not a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

This is a function. This is not a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

This is a function. This is not a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

This is a function. This is not a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

This is a function. This is not a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

Why are these functions? Why are these NOT functions?

MAKE A CONJECTURE

(c) 2013 Kathleen Strange

This is a function This is not a function

THINK ABOUT DOMAIN AND RANGE

(c) 2013 Kathleen Strange

Does each element of the domain correspond to exactly one element of the range?

If yes, then the graph represents a function.

UNDERSTANDING FUNCTIONS

(c) 2013 Kathleen Strange

IS THIS A FUNCTION? WHY OR WHY NOT?

(c) 2013 Kathleen Strange

Since the equation x^2 = 9 has two solutions, x = +3 and x = –3, students might think that sqrt(9) is +–3. However, if we want sqrt(x) to be a function of x, we need to choose one of these square roots. The square root function, g(x) = sqrt(x), is defined to be the positive square root of x for any positive x.

WHY ARE FUNCTIONS IMPORTANT?

http://ime.math.arizona.edu/progressions/