1. 2.2.2 – Using and Graphing Linear Functions

2. Recall, we had a test to tell whether something was a function What was the “visual” test?

3. Graphing With any function, you still may graph it The new notation, f(x), does not change our process for graphing Don’t always need a table; technically only need 2 points to make a line

4. Graphing Linear Functions When graphing linear functions, choose two values; Easiest values are usually x = 0 and x = 1 That’s all you need; lines always have the same “pattern”

5. Example. Graph the function f(x) = 2x - 1

6. Example. Graph the function f(x) = x + 5

7. Example. Graph the function f(x) = 4

8. Using Functions We have written our own equations for situations in terms of applications More often though, we need to write a function Why would using function notation be better than just an equation?

9. Make sure when you use functions: – 1) Double check the variable name – 2) Take a close look at the function name – 3) Plug in values only for the specified variable

10. Example. A particular gym uses the function c(t) = 50t + 60 to figure out fees; a $60 initial cost, and $50 per month. In the function c, t represents the time from signing up in the gym in months. How much would it cost to stay with the gym for 10 months?

11. Example. Using the previous information, how much would it cost over 2 years?

12. Domains Remember, the domain is the set of all numbers which you may use as input values for your functions or equations Sometimes, we need to be specific about the domain and any restrictions – Only for a certain period of time – Real limits – Make sense within context

13. Example. You agree to purchase a new car. The dealer requires a down payment of $2,000, followed by monthly payments of $400 for 4 years, at which point the car will be paid off. How much will you have paid after the 4 years, given the equation p(t) = 2000 + 400t, where t is the number of months for ownership?

14. Assignment Pg.76 28-36 even, 38-42, 43, 45, 48-51