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Unit 4: Functions

Unit 4: Functions Lesson 3

Lesson 4.03 Graphical Features of Functions

Students will be able to:

§ Content Objective: Define and Identify key features of functions based on a graph.

§ Language Objective: Discuss with classmates how to find key features of graphs.

The function 𝑔(𝑥) is shown graphed below. Using the graph, evaluate each of the following:

a. 𝑔(−1)

b. 𝑔(3)

c. 𝑔(−5)

d. 𝑔(𝑥) = 3

Function Notation

Function Definition

A relation is a function if each input has at most

__________ output.

Vertical Line Test

A graph represents a function if when you draw a

vertical line anywhere on the graph, it intersects at

most _______ time.

Warm Up

Vocabulary Review

Graphic Organizer

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Unit 4: Functions

Unit 4: Functions Lesson 3

Use the graph to answer the following questions.

a. Does the point (−5,4) represent a relative maximum or relative minimum?

b. Which point on the graph represents both a relative

minimum and the y-intercept?

c. How many x-intercepts are there? Circle them on the graph.

d. Is the graph increasing or decreasing over

the interval −5 < 𝑥 < 0?

e. State two other intervals where the graph is increasing and decreasing.

Increasing interval: _______________________________ Decreasing interval: _______________________________

Use the graph to answer the following questions.

a. Which point represents the relative maximum?

b. Which point represents the relative minimum?

c. How many x-intercepts are there? State one of them as an (𝑥, 𝑦)pair.

d. What is the y-intercept? State your answer as an ordered pair.

f. Is the graph increasing or decreasing over

the interval 2 < 𝑥 < 4?

g. State two other intervals where the graph is increasing and decreasing.

Increasing interval: _______________________________ Decreasing interval: _______________________________

Skill 1: Identifying Key Features of Graphs

Exercise 1: Identifying Key Features of Graphs

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Unit 4: Functions

Unit 4: Functions Lesson 3

Shown below is the graph of the function 𝑓(𝑥). a. State the relative maximum.

b. State the relative minimum.

c. The point (0,0) represents two key features of the

graph. List them below. ____________________ ____________________

d. State the x-intercepts as (𝑥, 𝑦) pairs. e. Why do you think another word for x-intercepts

is zeros?

f. State an interval where the graph is increasing. g. State an interval where the graph is decreasing.

Given the table below, answer the following questions.

a. Graph the points on the set of axes. Connect the points on the graph.

b. Which two points in the table represent the x-intercepts?

c. Which point represents the y-intercept? Explain how you know.

d. Does the turning point represent a maximum or minimum?

𝑥 𝑦

−2 0

−1 −3

0 −4

1 −3

2 0

Check Point

Talk it Out

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Unit 4: Functions

Unit 4: Functions Lesson 3

Name: ____________________________________________________________________ 1. Use the graph to answer the following questions.

a. How many minimum points are on the graph?

b. What is the maximum point?

c. What is the y-intercept? State your answer in (𝑥, 𝑦) form.

d. State the x-intercepts (zeros). e. Write an interval over the x-axis where the graph is increasing.

f. Write an interval over the x-axis where the graph is decreasing.

2. Stacy and Colleen are asked to analyze the graph below. Stacy says that the x-intercept is (0,0).

Colleen disagrees with Stacy and says that it represents the y-intercept. Who is correct? Explain.

Problem Set