Module 5 Topic A - 8theastviewmath.weebly.com€¦ · 5.1e Class Activity: More About Functions 1....
Transcript of Module 5 Topic A - 8theastviewmath.weebly.com€¦ · 5.1e Class Activity: More About Functions 1....
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.