2.2 Linear Functions and Function

NotationObjective: Identify, evaluate, and graph linear

functions

Linear FunctionA 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.

Linear Function

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

Function NotationBy 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.

Identify a Linear FunctionTell whether the function is linear. If not explain why.

1. f(x) = 2x – 9

2. f(x) = -3x

3. g(x) =

4. h(x) = 5

5. f(x) = x2+2x+1

Identify a Linear FunctionTell whether the function is linear. If not explain why.

a) f(x) = 4x – 3

b)

c)

Evaluate a FunctionEvaluate the function when x = -2

a. f(x) = -3x+7

b. g(x) = x2 + 2x – 10

Graphing Linear FunctionsGraph the function f(x) = 2x – 1

Graph h(x) = 4x – 1

Graphp(t) = -t – 2

Graphb(x) = -2x + 5

Real-world situationYou are joining a fitness club that charges a one-time membership fee of $25 and a monthly fee of $50.

a) Write a function that models your total membership cost.

b) Graph your function from part (a)

c) Use your function model to find the cost of membership for the first year.