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