MATH 1310 Session 4.

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MATH 1310 Session 4

Functions: Basic Ideas

Popper 4 3. 1. (-∞, 21] b. [21, ∞) c. (-∞, ∞) d. [4, ∞) 2.

Functions and Graphs

Does the graph represent a function

https://youtu.be/sOK4q4OcEQc

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 + 2x2 + 5. 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).

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

The following function passes through the point (8, -11). Is the function even or odd? What other point must it contain? What is a possible equation? (assume all letters represent constants) f(x) = ax3 + bx2 + cx + d h(x) = ax3 + bx g(x) = ax2 + b j(x) = ax2 + bx

Transforming Functions

Popper 4, continued: 𝑓 𝑥 =− 𝑥+2 −5 4. Identify the Parent Function: a. Linear b. Quadratic c. Rational d. Radical 5. Is there a vertical shift? a. up 5 b. up 2 c. down 5 d. down 2 6. Is there a horizontal (y-axis) reflection? a. Yes b. No 7. Is there a vertical (x-axis) reflection?

1.