1. DO NOW – You have 4 minutes to complete the problem below.

2. Focus QUEstion: How can we determine one-to-one functions and find the range of a function? December 12, 2013

3. DO NOW
How can we find the relation for the DO NOW?

4. Given f(x) = 2x + 1, find -4[f(3) – f(1)]
-40
-16 -8 4
Answer Now

5. MORE PRACTICE Evaluate f(t+2) for the function f(x) = x2 + 2x + 3
f(t+2) = (t+2)2 + 2(t+2) + 3
= t2 + 4t t
= t2 + 6t + 11

6. YOU TRY:

7. A function f is one-to-one if each element of the domain pairs to exactly one unique element of the range.
Must pass vertical and horizontal line test.

8. x1 y1 x1 y1 x2 y2 x2 x3 x3 y3 y3 One-to-one function NOT One-to-one
Domain
Range
Domain
Range
One-to-one
function
NOT One-to-one
function x1 y1 y2 x3 y3
Not a
function
Domain
Range

9. M: Mother Function is NOT one-one
Joe
Samantha
Anna
Ian
Chelsea
George
Laura
Julie
Hilary
Barbara
Sue
Humans
Mothers

10. S: Social Security function IS one-one
Joe
Samantha
Anna
Ian
Chelsea
George
Americans
SSN

11. Is the function f below one – one?10 11 12 13 14 15 16 1 2 3 4 5 6 7

12. Theorem Horizontal Line Test
If horizontal lines intersect the graph of a function f in at most one point, then f is one-to-one.

13. Use the graph to determine whether the function
is one-to-one.
Not one-to-one.

14. Use the graph to determine whether the function is one-to-one.

15. Exit Ticket
f (x) = 2x² - 2x + 1,  find  f (x+3)