Warm-Up Exercises 1. Evaluate for 5, 2, and 5. 7–2x2x – x = Find two ordered pairs on each line. 2x 3y = y = 3. ANSWER 17, 3, 3 –– ANSWER ( ),), 0, 3 () 5, 13 ANSWER ( ),), 0, 7 () 5, y5y–3x3x 15 = ANSWER ( ),), 5, 0 () 0, 3 –

Vocabulary Linear Functions and Function Notation An equation represents a linear function if it 1) contains no exponent higher than 1. 2) has no variables in the denominators of fractions. 3) has no variables under radicals.

Vocabulary Linear Functions and Function Notation Function notation is a way to identify functions. The notation is read “f of x” and signals that the expression is a function in which x is the independent variable. is another name for y.

Example 1 Identify a Linear Function Tell whether the function is linear. Explain. f x a. () +x 2x 2 +2x2x1 = c. = 4 h x ()– b. ) g x = ( x 1+x

Checkpoint Tell whether the function is linear. Explain. 1. 4x4x – 1 () f x = 2. 5 – x 3x 3 () g x = Identify a Linear Function 3. x 9 () h x = 4. 9 x () r x=

Example 2 Evaluate a Function Evaluate the function when x 2. – = a. 7 + f () x 3x3x – = b. 2x2x+ g () x = x2x2 – 10

Checkpoint Evaluate the function when x 3. = 5. 1 f () x 4x4x – = 6. + g () x = 2x 22x 2 – x3x p () x x 2x 2 = Evaluate a Function

Example 3 Graph a Linear Function Graph 1.1. f () x 2x2x – =

Write and Use a Linear Function Example 4 Fitness Clubs You are joining a fitness club that charges a one-time membership fee of $60 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.

Write and Use a Linear Function Example 4 b. Graph your function from part (a). c. Use your function model to find the cost of membership for the first year.

Checkpoint Graph the function h () x 4x4x – = Graph a Linear Function

Checkpoint Graph the function. 9. p () t = t – 2 – Graph a Linear Function

Checkpoint Graph the function s () x 2x2x = +– Graph a Linear Function

Checkpoint 11. For the club in Example 4, find the cost of membership for the first two years. Graph a Linear Function

Linear Functions and Linear Notation Homework Homework: Page 76 #15-35 odd, 38-42, Page 79 #62-67