Module 5

Topic A

8th Grade Math

Note Packet

Name

__________________

Period _________

In order to be a function all ______- values must be ___________.

We looked at the ________ and compare rates from ________,

_________, and ___________.

Linear functions are written in ____________ or has an exponent

raised to a power of ________.

__________ functions has an exponent greater than 1 or has and

______ in the denominator.

Domain and Range Notes

Vocabulary Words

Domain is all the ______ values. It is the _____________ variable.

It is also the ______________ of the function.

Range is all the ______ values. It is the _______________ variable. It is also

the ________________ of the function.

Discrete Graph - a graph whose points _______ ________ connected.

Continuous Graph – a graph whose points _________ connected.

Dependent Independent Input Discrete

X Y Output Continuous

________________ Graph ________________ Graph

-1

2

3

2

4

6

There are many different ways that you will see domain and range written. Let’s

review some of the ways we’ve seen discrete functions represented. A discrete

function is one where the points are not connected to each other. If you graphed

either of the functions below, it would just be a bunch of points.

The type of function you have will help you decide how to write the domain and

range.

If your function is represented as a list of ordered pairs, a table, or a map, the

best way to list your domain and range is using { }.

Example 1: Write the domain and range for the following function:

(0, 2) (1, -5) (2, 8) (3, 10)

Domain: {0, 1, 2, 3}

Range: {-5, 2, 8, 10}

Look at the problem above and write down the domain and range for that function.

Left: Right

D: D:

R: R:

State the domain and range of each relation.

{(1, 3), (2, 4), (3, 3), (4, 4)}

Domain: { }

Range: { }

X Y

0 3

2 6

4 12

0

1

3

9

-5

4

8

14

Domain: { }

Range: { }

3.

Since these functions are all discrete (they are just specific points, not continuous

lines) we have to list the values for x and y.

A continuous function is one that can be graphed as a smooth line or curve. When

the function is a line, we can’t list values because we would have to list every single

decimal – an impossible thing to do! We need to use a different notation.

Look at the graph to the left.

See how it is a line?

It also has two endpoints: one is at

(-7, -3), and the other is at (4, 7).

Our domain includes all the values from -7

to 4, and the range includes all the values

from -3 to 7. But how do we write that? And

how do the endpoints change things?

The domain can be written as:

D: ________ ≤ x ≤ _________

The x values are between the numbers, so that’s where the x

goes.

In the blanks, put the smallest x value and the largest x

value. Because the endpoints of our graph are included (they

are filled in circles), we use the ≤ symbol to show that they

are valid numbers in the domain.

Try writing the range: R: ________ ≤ y ≤ __________

Domain: { }

Range: { }

Look at the graph to the right.

What do you notice that’s different from

the previous graph?

What symbols do you think we should use

when writing the domain and range of this

graph? Remember from graphing inequalities

– an open circle goes with the < or > sign, and a

closed circle goes with the ≤ or ≥ sign.

Now write the domain and range for this

function. Make sure you use the correct sign at the correct end!:

D: _______________ R: _________________

Remember domain and range must always go from smallest to largest when you have

two endpoints.

Another type of graph you may see looks like this:

What do the arrows on the ends of the

graph mean?

Is this a discrete or continuous graph?

Since the graph goes on forever at

either end, it will cover all x values. We

write this domain as x = all real numbers. You can use a capital R with an extra

thick vertical line. Some people write a domain like this as

D: -∞ < x < ∞

The range is a little different, because our graph has a maximum point but no

minimum. Our range is all numbers less than or equal to 4.

R: y ≤ 4

Now try one on your own:

D: _______________________

R: _______________________

Summary:

Domain is all the ______ values. It is the _____________ variable.

It is also the ______________ of the function.

Range is all the ______ values. It is the _______________ variable. It is also

the ________________ of the function.

___________-Graph - a graph whose points are not connected.

___________ Graph – a graph whose points are connected.

5.1e Class Activity: More About Functions

1. Paradise Valley Orchards has the banner shown hanging from their store window. Sally is

trying to determine how much she will spend depending on how many bushels of apples she

purchases.

a. Write an equation that gives the amount Sally will spend y depending on how

many bushels of apples x she purchases.

b. Complete the graph and table below for this relationship.

c.

We know from the previous lessons, that the relationship between number of bushels purchased

and amount spent is an example of a function. The equation above gives us a rule for how to

determine the amount of money spent based on the number of bushels purchased.

In a functional relationship represented with an equation, the independent variable represents

the input or x-value of the function and the dependent variable represents the output or y-value

of the function. In a function, the dependent variable is determined by or depends on the

independent variable. In our example above the independent variable is the number of bushels

purchased and the dependent variable is the amount of money spent. The amount of money one

spends depends on the number of bushels one purchases. Another way to say this is that the

amount of money spent is a function of the number of bushels purchased.

If we think of our input machine, we are inputing the number of bushels purchased and the

machine takes that number and multiplies it by 15 to give us our output which is the amount of

money we will spend.

Number of

Bushels

x

Amount Spent

(dollars)

y

1 BUSHEL OF APPLES FOR

ONLY $15

2. Miguel is taking a road trip and is driving at a constant speed of 65 mph. He is trying to

determine how many miles he can drive based on how many hours he drives.

a. Identify the independent variable in this situation:

_____________________________

b. Identify the dependent variable in this situation:

____________________________

c. Complete the graph and table below for this relationship. Make sure you label the

columns and axes in your table and graph.

d. Write an equation that represents this situation:

_____________________________

e. In this situation ______________________ is a function of

_________________________.

x

y

3. The drama club is selling tickets to the Fall Ball. They use $2 from each ticket sale for food

and decorations.

a. Identify the independent variable in this situation:

__________________________

b. Identify the dependent variable in this situation: _________________________

c. Create a table, graph, and equation for this function.

Equation: ______________________

d. Complete the following sentence for this situation.

________________________________ is a function of

________________________________.

4. The average cost of a movie ticket has steadily increased over time.

a. Identify the dependent and independent variables in this functional relationship.

b. Sketch a possible graph of this situation.

x

y

5. Susan is reading her history text book for an upcoming test. She can read 5 pages in 10

minutes. Susan is interested in determining how many pages she can read based on how long

she reads for.

a. Identify the independent variable in this situation: ______________________

b. Identify the dependent variable in this situation:

____________________________

c. Create a representation (table, graph, equation) of this function in the space

below.

6. Chris is also reading his history text book for an upcoming test and can also read 5 pages in

10 minutes. However, Chris is interested in determining how long it will take him to read

based on how many pages he has to read.

a. Identify the independent variable in this situation:

_____________________________

b. Identify the dependent variable in this situation:

____________________________

c. Create a representation (table, graph, equation) of this function in the space

below.

Directions: Each of the following situations represents a functional relationship between two

quantities. Determine the dependent variable and the independent variable. The first one has

been done for you.

7. In warm climates, the average amount of electricity used rises as the daily average

temperature increases and falls as the daily average temperature decreases.

8. The number of calories you burn increases as the number of minutes that you walk increases.

9. The air pressure inside a tire increases with the temperature.

10. As the amount of rain decreases, so does the water level of the river.

11. The total number of jars of pickles that a factory can produce depends on the number of

pickles they receive.

12. The weight of the box increases as the number of books placed inside the box increases.

We learned how to write equation in ______________ from word problems.