Go Over HW Answers: Domain & Range HW WKS Write out answers to HW

Unit 2: Graphical Analysis of Functions 2.1 Graphs of Basic Functions & Relations – Part 1

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

Continuity (Informal Definition): 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 A function is said to be increasing on an interval if the y-value increases as the x-value increases. When x1 < x2, f(x1) < f(x2), f is increasing.

Decreasing Function A function is said to be decreasing on an interval if the y-value decreases as the x-value increases. When x1 < x2, f(x1) > f(x2), f is decreasing.

Constant Function A function is said to be constant on an interval if its graph is a horizontal line over the interval. For any x1 and x2, f(x1) = f(x2), f is constant.

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

Parent Function: 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 Pass out the parent function packet at this point and do the first function (identity) with the class using the document camera. Then have the students work in groups and have them do one function per group. Have each group write out the answers on the chart paper (provide them with a large grid). Then do a gallery walk when they are all done so they can fill out their packets. They should finish this by the following day. 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 |