1. Section 3.2 https://www.youtube.com/watch?v=Ybol2aRvmRU
MATH 1310
Section 3.2

2. Functions and Graphs

3. Popper 10: Does the graph represent a function? a. Yes b. No1. 2.

4. 4. 3.

8. Identity Function
y = x
Constant Function
y = k

9. Quadratic Function
Cubic Function

10. Absolute Value Function
Radical Function

11. Rational Function
Cube Root Function

16. For 𝑓 𝑥 = 5 2𝑥+4 evaluate 𝑓 𝑎+1 𝑎−1

17. For 𝑔 𝑥 = 𝑥 2 +2𝑥−1 evaluate 𝑔 5 𝑏

18. Popper 11:
1. P(-2)
2. P(2)
3. P(3) 2
b. 4
c. -3
d. 9

20. Odd and Even Functions:
Odd Functions have only odd exponents, such as f(x) = 2x3 + 8x. They satisfy the formula: f(-x) = -f(x) They are symmetric about the origin. If they contain the point (a, b) they also contain (-a, -b). Even Functions only have even exponents, such as g(x) = 3x4 + 2x They satisfy the formula: g(-x) = g(x) They are symmetric about the y-axis. If they contain the point (a, b), they also contain (-a, b).

21. An even function contains the point (-5, -2).
What point must it also contain? What is a possible graph of the function?

22. Popper 11, continued The following function passes through the point (8, -11).
4. Is the function even or odd? a. even b. odd c. neither 5. What other point must it contain? a. (-8, -11) b. (-8, 11) c. (8, 11) d. (-11, 8) 6. What is a possible equation? (assume all letters represent constants) a. f(x) = ax3 + bx2 + cx + d c. h(x) = ax3 + bx b. g(x) = ax2 + b d. j(x) = ax2 + bx

23. Determine the value of the difference quotient for f(x) = -4x + 5
The difference quotient is: 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ

24. Determine the value of the difference quotient for f(x) = 2x2 + 3x – 1
The difference quotient is: 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ