Algebra 2

3-8 Functions

3-8 Functions

WARMUP

Complete the table:

x 4 – 2x (x, y)

-1 4 – 2(-1) (-1, 6)

0

1

2

3

3-8 Functions

A function is a correspondence between two sets, D and R, that assigns to each member of D exactly one member of R.

Real world example:

Post Office: The cost of mailing a letter is a function of its weight – the heavier it is, the more it will cost to mail. There is a correspondence, cost to weight, given by a definite rule.

3-8 Functions

Another example.

Paul VI has a grade scale – a letter grade is a function of the numeric grade earned by the student. There is a correspondence, letter grade to numeric grade, given by a definite rule.

Can you think of any other examples?

3-8 Functions

You can think of functions as a machine, that you put something in, and get something out on the other side, based on rules inside the machine.

3-8 Functions

National Library of Virtual Manipulatives:

http://nlvm.usu.edu/en/nav/vlibrary.html

Check out the Function Machine…

Another cool one:

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=133

3-8 Functions

Again, a function is a correspondence between two sets, D and R, that assigns to each member of D exactly one member of R.

3-8 Functions

Mapping diagrams in book…

3-8 Functions

The set D is the domain of the function.

The range of the function is the is the set of all members of R assigned to at least one member of D.

Note: Unless otherwise stated, domains and ranges in our book will be sets of Real numbers.

3-8 Functions

So, an example of a rule for a function might be:

“double the number.”

-2 -4-1 -20 01 22 4

3-8 Functions

The letters f, g, F, G, and occasionally , (Greek phi) are used to name functions.

In the book you might see arrow notation:

g: x 2x

This is read “g, the function that assigns to x the number 2x”

3-8 Functions

The graph of a function ƒ is the set of all points (x, y) such that x is in the domain of ƒ and the rule of the function assigns y to x.

The values of a function are the members of it’s range. If g: x 2x then g assigns to 2 the value 4.

Functional notation: write g(x) = 4

3-8 Functions

f(2) = 4, read “the value of f at 2 is 4” or more commonly, “f of 2 is 4”

In general:

f(x) denotes the value of f at x

BE CAREFUL: f(x) DOES NOT MEAN f multiplied by x!!!

3-8 Functions

Domains and ranges.

IMPORTANT: The domain of a function is the set of those

real numbers for which the equation produces real numbers!

What are the domains of the following:

2

1 1( ) g(x)= h(x)= 2

4 ( 2)f x x

x x x

3-8 Functions

The range of functions are the values that can come out of the function:

What are the ranges of the following functions:

2

1 1( ) g(x)= h(x)= 2

4 ( 2)f x x

x x x

3-8 Functions

More practice…

Homework