WARM UP Solve the equation 1 4 x

WARM UP Solve the equation 1. 4 x + 8 = 24 2. 3 x – 5 x = -12 3. 3 x + 9 = 9 x - 7 3

WARM UP Solve the equation 1. x + 6 = 14 2. 9 – y = 4 3. 4 x + 5 y =15 2

WARM UP Solve the equation 1. x + 6 = 14 2. 9 – y = 4 3. 4 x + 5 y =15 1

WARM UP Solve the equation 1. x + 6 = 14 2. 9 – y = 4 3. 4 x + 5 y =15 0

4. 8 Functions and Relations Today’s Schedule: • Lesson 4. 8 Powerpoint • In class assignment/homework • Exit Slip GOAL: Decide whether a relation is a function and use function notation. KEY WORDS: relation, function, vertical line test, function notation, linear function.

4. 8 Functions and Relations FUNCTION NOTATION When a function is defined by an equation, it is often convenient to name the function. Just as x is commonly used as a variable, the letter f is commonly used to name a function. To write a function using FUNCTION NOTATION, you use f(x) in place of y. x-y notation: y = 3 x + 2 function notation: f(x) = 3 x + 2

4. 8 Functions and Relations EXAMPLE 3: Evaluate a Function Evaluate f(x) = 2 x -3 when x = -2 SOLUTION You can evaluate a function for a given value by substituting the iven value for the variable and simplifying. • Write the original function. • Substitute -2 for x. • Simplify.

4. 8 Functions and Relations CHECKPOINT: Evaluate a Function a. Evaluate f(x) = 4 x + 5 when x = 2 b. Evaluate g(x) = x 2 when x = 3

4. 8 Functions and Relations LINEAR FUNCTION A function is called a linear function if it is of the form f(x) = mx + b. For instance, the function in Example 3 part a is linear. But, the function in Example 3 part b is not linear. To graph a linear function, rewrite the function using x-y notation.

4. 8 Functions and Relations EXAMPLE 4: Graph a Linear Function Graph f(x) = -2 x + 3 SOLUTION • Rewrite the function in x-y notation. • Find the slope and the y-intercept • Use slope to find a second point • Draw a line through the two points