Alg2 Lesson 3.7: Rational Function

Lesson 3.7: Rational Functions

Obj: I can formulate and graph rational functions.

EQ: How do I use asymptotes to graph rational functions?
How do I formulate rational equations given a verbal
description?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Poll

What is your goal for this lesson?

• Learn more about fractions.

• Gain a greater interest in cooking.

• To get a 100 1st try.

• To cultivate a love for reading.

Part 1: Formulate Rational

Functions from Word Problems

Fill in the Blanks

A group of 6 friends shared a pizza equally. If there were ¾ of the pizza left after
they each took a slice, how many slices were in the pizza originally?

slices

Multiple Choice

If 3/5 of a garden is planted with carrots and 1/4 is planted with strawberries, what
fraction of the garden is not planted?

• 1/2
• 3/20
• 5/9

• 4/5

Multiple Choice

If a recipe calls for 3/4 cup of flour and you want to make half of the recipe, how
much flour do your need?

• 1/2 cup of flour
• 6/4 cups of flour

• 1/4 cup of flour
• 3/8 cup of flour

Fill in the Blanks

The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cm³ under pressure of 32 kg/cm². What will be its volume under pressure of 40 kg/cm²?

cm³

Multiple Choice

Jenny’s mom says she has an hour before it’s bedtime. Jenny spends 3/5 of the hour texting a
friend and 3/8 of the remaining time brushing her teeth and putting on her pajamas. She spends
the rest of the time reading her book. How long did Jenny read?

• 15 min
• 10 min
• 20 min
• 5 min

Fill in the Blanks

Working together, Joe and Dan can sweep a porch in 4.8 minutes. Had he done it alone it would have taken Dan 12 minutes. Find how long it would take Joe to do it alone.

minutes

Multiple Choice

9 kg of generic sugar was made by combining 6 kg of brand X sugar which costs $4/kg with 3 kg of brand Y sugar which costs $1/kg. Find the cost per kg of the mixture.

• $2/kg
• $2.50/kg

• $3/kg
• $4/kg
• $6/kg

Word Cloud

Where would you like to travel to?

Part 2: Characteristics of

Rational Functions

From Graph

From Graph

From Equation

Labeling

Find the coordinate of each hole.

Drag labels to their correct position on the image

3

-2

4

1

1/11

-4

Labeling

Find each vertical asymptote.

Drag labels to their correct position on the image

t = 5/7

none

t = 2

q = 1

w = ±2

w = ± 4

Labeling

Find each horizontal asymptote.

Drag labels to their correct position on the image

y = 1

y = -1

none

y = 0

y = 4

Part 3: Formulate Rational

Functions from Graph

Form: y = a/(x - h) + k

h is the vertical asymptote

k is the vertical asymptote

Identify a point to plug into
equation to solve for a.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.