Download Linear Function

Functions & Relations II
Unit 4
Answers to Definition of a Function WS HW
1. No
2. yes
3. yes
4. No
5. no
6. yes
7. Yes
8. any but 5, 7, 9
9. no
10. Yes
11. no
12. yes
13.28
14. 11
15. 10
16. Yes
17. any but 1, 2, 3
18. yes
19. 22
20. 9
21. 98
When you are finished get a white board,
marker, and eraser.
Ticket Out the Door
• You did well except for a couple things.
– Mapping diagrams
• Do not list numbers twice
– Graphing
• The + in the middle is the x axis and y axis.
Take the x & y beside each other and plot
all of the points on your whiteboard.
x
y
-3
-2
-1
0
1
2
3
-3
-1
1
3
5
7
9
Plot (-3, -3) on your whiteboard.
You should have 7
points. When you
are done, connect
them together.
Does yours look like this?
You just created a linear function.
• It is LINEAR because it is a straight, continuous
line. Get it LINE, LINEAR. A line like a V is not
continuous.
• FUNCTION because it passes the Vertical Line
Test. It also does not have any repeating x’s.
• Let’s look back at the T-chart to see if we
notice anything special. Recognize any
patterns?
Do you notice a pattern between the x’s?
What about the y’s?
x
+1
+1
+1
+1
+1
+1
-3
<
-2
<
-1
<
0
<
1
<
2
<
3
y
-3 > +2
-1 > +2
1 > +2
3 > +2
5 > +2
7 > +2
9
Graph each of the sets of ordered pairs on the
whiteboard.
Is it linear (in a line)? Is it a function?
Have us check it before going to the next one.
a. {(0,1), (0,-1), (-1,1), (-1,2)}
b. {(2,2), (3,3), (4,3), (5,3)}
c. {(2,3), (3,4), (4,5), (5,6)}
a.Not linear; not a function
b.Not linear; a function
c.Linear; a function
Now, look for the patterns of the x’s and the y’s
in the sets of ordered pairs.
Write the ordered pairs in a T-chart.
If you are stuck, look for the pattern between
the x’s and then the y’s.
a. {(0,1), (0,-1), (-1,1), (-1,2)}
b. {(2,2), (3,3), (4,3), (5,3)}
c. {(2,3), (3,4), (4,5), (5,6)}
Linear Function
(Yes, these are notes. Please write them down.)
• It is LINEAR because it is a straight,
continuous line. Get it? LINE, LINEAR.
• FUNCTION because it passes the Vertical Line
Test.
• In a set of ordered pairs, you can determine if
it is linear if there is a pattern between all of
the x’s and another pattern between all of
the y’s.
Linear Function Equations
There is no black, bold, and underlined below,
but I want you to write it anyway.
You can check it by doing a T-Chart
or you can just trust me.
y3= x – 4 Non-linear (has an exponent)
y= x4 + 3 Non-linear (has an exponent)
y= 4x + 3 Linear (no exponent except
understood 1)
y= -2
x= 5
Function (horizontal line) and linear
Non-function (vertical line) but linear
What makes it linear?
• There has to be a common difference
between all of the x’s and a common
difference between all of the y’s.
• Also, it is a straight continuous line.
• Which line is linear but NOT a function?
•
A VERTICAL line. All other lines are
vertical functions.
Word Problems
• At 6000 ft in the air, the temperature is 0
degrees Celsius. Every 1000 ft down, the
temperature rises 7 degrees. Create a table
and graph to find the temperature at sea level
(0 ft above sea level). Is this a representation
of a linear function? Why or why not?
Is it a linear function?
x
y
6000
0
5000
7
4000
14
3000
21
2000
28
1000
35
0
42
Is it a function?
Any repeating x’s?
Is it linear?
Do the x’s and y’s
have a pattern?
Word Problem
A cab fare is $4.00 base fee and $0.30 per mile. Find
the cost of driving 5 miles. Is this relation a function?
Explain.
• I can write the equation for this.
y = 4 + .30x
(You should be able to do the equation because of what we did
from Unit 3.)
Make a T-Chart. Let’s look at the next slide.
y = 4 + .30x
• Let’s plug in some numbers.
x
y
1
4.30
2
4.60
3
4.90
4
5.20
But what is the answer?
• Answer: Yes, this is a function because when I
plug in my numbers for x, each input (x) has a
unique output (y). None of the x’s repeat.
• Also, is it linear? What makes it linear?
Remember that linear means that the
difference between the x’s are the same AND
the differences between the y’s are the same.
Now you have all the information to
do your homework.
• You are to finish your Unit 4 Study Guide by
Wednesday.
• Also on Wednesday, I will hand out an
optional extra credit project.