1. Define evaluate and compare functions
Algebra: 5.01/ functions 8.f.1,.2,.3
Define evaluate and compare functions
-Translate various representations of functions and identify relations as linear or nonlinear

2. Vocabulary
Function- A rule that relates two quantities so that each input value corresponds to exactly one output value
Input-The value substituted into an expression or function
Output- The value that results from the substitution of a given input into an expression or function

3. Vocabulary Domain- The set of all possible input values
Range- The set of all possible output values
Function Notation- The notation used to describe a function.
Ex. y=3x2  f(x)= 3x2
f(x) is read “f of x”

4. Representation
Tables
Graphs
Equations

5. Representations x x2+1 y -2 -1 1 2 (-2)2+1 (-1)2+1 (0)2+1 (1)2+1
Make a table of inputs and outputs
Use the table to make a graph x
x2+1 y -2 -1 1 2
(-2)2+1
(-1)2+1
(0)2+1
(1)2+1
(2)2+1 5

6. x y 1 2 3 5 4 This IS a Function! Identify a Function
To determine if a relationship is a function, verify that each input has exactly ONE output x y 1 2 3 5 4
One x value has one y value.
This IS a Function!

7. Identify a Function The relationship is NOT a function!
The input x=0 has two outputs, y = 3 and y = -3.
Other x values also have more than one y value.
The relationship is NOT a function!

8. Identify a Function x y -2 -1 1 2 (-2)2=4 (-1)2=1 (0)2=0 (1)2=1 (2)2=4
Make an input-output table and use it to graph y=x2 x y -2 -1 1 2
(-2)2=4
(-1)2=1
(0)2=0
(1)2=1
(2)2=4
Each input, x, has only one output, y.
The relationship IS a function.

9. Function Notation The output value of the function, f that
corresponds to the input value x is written, f(x)
The expression f(x) means “the rule of f applied to the value of x.
Not f multiplied by x

10. F(1) = 12 = 1 y= x2  = f(x)=x2 Function Notation
The output y is the rule of f applied to x
F(1) = 12 = 1
F(1) means evaluate f(x) for x = 1

11. Evaluating Functions For each function, find f(0), f(2), and f(-1)
Y= 2x - 1
f(x)=
2x - 1
f(0)=
2(0) – 1
=-1 3
f(2) =
2(2) – 1 =
f (-1)=
2(-1) – 1 = -3

12. Evaluating Functions f(x)= y f(0)= -4 f(2) = -2 f (-1)= -5
Read the graph to find y for each x
f(x)= y
f(0)= -4
f(2) = -2
f (-1)= -5

13. Evaluating Functions x y -1 1 2 3 - 1 5 8 11 f(x)= y f(0)= 2 f(2) = 8
Read the table to find y for each x x y -1 1 2 3
- 1 5 8 11
f(x)= y
f(0)= 2
f(2) = 8
f (-1)= -1