Go Over HW Answers Domain Range HW WKS

Go Over HW Answers: Domain & Range HW WKS

Unit 2: Graphical Analysis of Functions 2. 1 Graphs of Basic Functions & Relations – Part 1

Objectives and HW: The students will be able to: n Give the informal definition of continuity; n Identify the basic parent functions and the domain and range of each; n Give domain intervals where function in continuous, increasing, decreasing, and constant. n HW: p. 92: 12 -34 (even)

Continuity (Informal Definition): n A function is continuous over an interval of its domain if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper.

Continuity Example: Give the interval(s) over which the following function is continuous. Give answers in interval notation. ○

Increasing Function n A function is said to be increasing on an interval if the yvalue increases as the x-value increases. n When x 1 < x 2, f(x 1) < f(x 2), f is increasing.

Decreasing Function n A function is said to be decreasing on an interval if the y -value decreases as the x-value increases. n When x 1 < x 2, f(x 1) > f(x 2), f is decreasing.

Constant Function n A function is said to be constant on an interval if its graph is a horizontal line over the interval. n For any x 1 and x 2, f(x 1) = f(x 2), f is constant.

On what interval is the given function increasing? decreasing? constant? (Give answers in interval notation. ) n Increasing: [2, ∞) n Decreasing: [-8, -4] n Constant: [-4, 2]

Parent Function: n n n A parent function is a function with a certain shape that has the simplest algebraic rule for that shape. The following are the different types of parent functions and their graphs. Identify the following: ¨ Domain ¨ Range ¨ Interval(s) where the function is continuous ¨ Interval(s) where the function is increasing ¨ Interval(s) where the function is decreasing

CONSTANT FUNCTION Identify the following: D: R: Cont: Inc: Dec: f(x) = 2

IDENTITY FUNCTION f(x) = X

SQUARING (QUADRATIC) FUNCTION f(x) = x 2

CUBING (CUBIC) FUNCTION f(x) = x 3

SQUARE ROOT FUNCTION f(x) =

CUBE ROOT FUNCTION

ABSOLUTE VALUE FUNCTION f(x) = | x |