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

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.

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

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.

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

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

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

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

Graph h(x) = 4x – 1

Graph p(t) = -t – 2

Graph b(x) = -2x + 5

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.