Domain and Range of Graphs, Functions

Objective

For students to be able to identify the domain and range by looking at a graph and understand how to see if a relation is a function.

Warm-Up

Have homework on the overhead. As students come in, instruct them to get out their homework and check their answers.

Encourage students to work together to come up with solutions to those problems they got wrong.

Go over the homework with the entire class.

Ask – “Are there any questions on your quiz?”

“What is going to be on your quiz?”

“Are number lines and finding the distance between two points going to be on your quiz?”

“Are graphing ordered pairs going to be on your quiz?”

“Are identifying the coordinates of a Cartesian plane going to be on the quiz?”

“How are the quadrants labeled?”

“If I have some x-values and some y-values, what are the different ways I can represent them? On a graph, chart, as ordered pairs?”

“Are inverses going to be on your quiz? What is an inverse?”

Gather homework and stamp sheet before disturbing the quiz.

Hand out the quiz.

Let students take the quiz.

Teacher Input – Guided Practice

When students are finished with the quiz, put up a 5-6 notes transparency.

Have students look at number 1. Ask them to make and x-y chart for the values.

Work through the worksheet with students.

Ask – “What is the domain of number x?”

“What is the range of number x?”

“Is 1.1 in the domain/range?”

“Is 1.2 in the domain/range?”

“Can someone generalize this?”

“How would we write this an inequality?”

“Does the same hold true for y-values?”

Teacher Input

Write ‘function – an equation that is 1:1 and onto’ on the overhead

Write ‘vertical line test’ on the overhead.

Ask ‘who can tell me what this means in terms everyone can understand?’

If you get any ideas, write them down. Then ask the students, ‘is anyone sure?’

Determine the terms students are unsure about and explain that we will research these terms.

Terms – function, equation, 1:1, onto, and vertical line test

Guided Practice

Break students into groups of three or four. * Decided on groups before class *

Assign each group a word and give them resources to find a definition for their word.

Groups with the vertical line test should get a Shodor website with the vertical line test applet to play with and make a generalization.

Bring groups with the same word together and have them discuss their findings and agree upon one definition.

Come back together as a class and discuss 1:1, onto, equation, function, and vertical line test

Make sure major points are hit – f(x) and v.l.t. applet

Work through problems 5 and 9 on homework 5-7.

Work through problems 13 and 19 on homework 5-7.

Independent Practice

Students should have time at the end of class to work through their homework problems with other students.

If they finish, students can play with the Shodor applet or look through the other materials.

Closure

Review the definition of a function and how to test it.

Review how to get the domain and range from a graph.

Remind them of their homework 5-6 and 5-7 evens.