1. 2.2 Linear Functions and Function Notation
Objective: Identify, evaluate, and graph linear functions

2. Linear Function
A linear function is a function of the form y = mx+b where m and b are constants, such as y = 2x+1
The graph of a linear function is a line.

3. Linear Function In order to be a linear function:
x cannot have an exponent greater than 1
x cannot appear in the denominator

4. Function Notation
By naming a function “f” you can write it using function notation
f(x) = mx+b
Read as “the value of f at x” or “f of x”
Note: a function does not have to be named by the letter f. You can also use other letters such as g or h.

5. Identify a Linear Function
Tell whether the function is linear. If not explain why.
f(x) = 2x – 9
f(x) = -3x
g(x) =
h(x) = 5
f(x) = x2+2x+1

6. Identify a Linear Function
Tell whether the function is linear. If not explain why.
f(x) = 4x – 3

7. Evaluate a Function Evaluate the function when x = -2 f(x) = -3x+7
g(x) = x2 + 2x – 10

8. Graphing Linear Functions
Graph the function f(x) = 2x – 1

9. Graph h(x) = 4x – 1

10. Graph p(t) = -t – 2

11. Graph b(x) = -2x + 5

12. Real-world situation
You are joining a fitness club that charges a one-time membership fee of $25 and a monthly fee of $50.
Write a function that models your total membership cost.
Graph your function from part (a)
Use your function model to find the cost of membership for the first year.