Functions Planner: Understanding Equations & Functions Relationship

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