1. 12.1 functions Copy planner

2. functions Functions are basically the same as equations, they are just written differently. F(x) means the function of “x” – What value of “x” to use Y = 2x – 4 (equation) F(x) = 2x – 4 (function) Instead of have a “y” value, you use the f(x) to show what the function would equal with a specific value.

3. function A function of “x” is a relationship in which no 2 ordered pairs have the same x-value 3 types of functions to recognize – Linear function – Quadratic function – Exponential function A graph that is not a function will have “x” values that are the same

4. Domain & range Domain: all x-values that can be input into a function. Range: the y-values or the “output” of the functions Function or not a function (1,6) (3,6) (3,7) (8,9) (1,6) (2,6) (3,7) (8,9)

5. Evaluating a function F(x) = 2x – 3 X = -2 Input -2 everywhere there is an “x” F(-2) = 2(-2) – 3 F(-2) = -7 F(0) = F(0) = -3

6. Real life functions Functions are often used by companies to determine how to price their products. X = cost of materials Pricing function f(x) = 2x + 10 X = 8 F(8) = 2(8) +10 F(8) = $26 So, if the business spends $8 to make an item, they would charge a customer $26 to buy it.

7. review What can a function NOT have? No 2 ordered pairs w/the same x-value What is the domain? X-values What is the range? Y-values

8. 12.2 linear functions Linear function in slope-intercept form: F(x) = mx + b To write an ordered pair in function notation f(-2) = 4 is the same as (2, -4)

9. Linear functions Find a function for f(2) = 5 and f(6) = 3 Remember, this is the same as having 2 points (2,5) and (6,3) Find the slope M = -1/2 Substitute the slope into the function & 1 of the point to solve for the y-intercept, b What is the function? F(x) = -1/2(x) + 6 When in doubt, treat like a regular equation

10. Let’s try some