Transcript 12-2

Check 12-1 HW
12-2 Graphing Functions
th
6
Grade Math HOMEWORK
Page 608
#7-20
Course 1
12-1 Tables and Functions
Our Learning Goal
Students will
understand functions
by creating tables and
graphing translations.
Course 1
12-1 Tables and Functions
Students will understand functions by creating
tables and graphing translations.
• Learn to use data in a table to write an equation for a
function and to use the equation to find a missing value.
• Learn to represent linear functions using ordered pairs
and graphs.
• Learn to use translations to change the positions of
figures on a coordinate plane.
• Learn to use reflections to change the positions of
figures on a coordinate plane.
• Learn to use rotations to change positions of figures on a
coordinate plane.
• Learn to visualize and show the results of stretching or
shrinking a figure.
Course 1
12-2 Graphing Functions
Today’s Learning Goal Assignment
Learn to represent
linear functions
using ordered
pairs and graphs.
Course 1
12-2 Graphing Functions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
12-2 Graphing Functions
Warm Up
Write an equation for each function. Tell what
each variable you use represents.
1. The length of a wall is 4 ft more than
three times the height.
l = 3h + 4, where l is length and h is height.
2. The number of trading cards is 3 less
than the number of buttons.
c = b – 3, where c is the number of cards
and b is the number of buttons.
Course 1
12-2 Graphing Functions
Problem of the Day
Steve saved $1.50 each week. How
many weeks did it take him to save
enough to buy a $45 skateboard?
30
Course 1
12-2 Graphing
Insert Lesson
Title Here
Functions
Vocabulary
linear equation
Course 1
12-2 Graphing Functions
Additional Example 1: Finding Solutions of
Equations with Two Variables
Use the given x-values to write solutions
of the equation y = 4x + 2 as ordered
pairs. x =1, 2, 3, 4.
Make a function table by
Write these
using the given values for x
solutions as
to find values for y.
ordered pairs.
Course 1
x
1
4x + 2
4(1) + 2
y
6
(x, y)
(1, 6)
2
3
4
4(2) + 2
4(3) + 2
4(4) + 2
10
14
18
(2, 10)
(3, 14)
(4, 18)
12-2 Graphing Functions
Try This: Example 1
Use the given x-values to write solutions
of the equation y = 3x + 2 as ordered
pairs. x = 2, 3, 4, 5.
Make a function table by
using the given values for x
to find values for y.
Course 1
Write these
solutions as
ordered pairs.
x
2
3
3x + 2
3(2) + 2
3(3) + 2
y
8
11
(x, y)
(2, 8)
(3, 11)
4
5
3(4) + 2
3(5) + 2
14
17
(4, 14)
(5, 17)
12-2 Graphing
Insert Lesson
Title Here
Functions
Check if an ordered pair is a
solution of an equation by putting
the x and y values into the
equation to see if they make it a
true statement.
Course 1
12-2 Graphing Functions
Additional Example 2: Checking Solutions of
Equations with Two Variables
Determine whether the ordered pair is a
solution to the given equation.
(3, 21); y = 7x
y = 7x
?
21 = 7(3)
Write the equation.
Substitute 3 for x and 21 for y.
?
21 = 21 
So (3, 21) is a solution to y = 7x.
Course 1
12-2 Graphing Functions
Try This: Example 2
Determine whether the ordered pair is a
solution to the given equation.
(4, 20); y = 5x
y = 5x
Write the equation.
?
20 = 5(4)
?
20 = 20
Substitute 4 for x and 20 for y.

So (4, 20) is a solution to y = 5x.
Course 1
12-2 Graphing
Insert Lesson
Title Here
Functions
You can also graph the solutions of
an equation on a coordinate plane.
When you graph the ordered pairs
of some functions, they form a
straight line. The equations that
express these functions are called
linear equations.
Course 1
12-2 Graphing
Insert Lesson
Title Here
Functions
Additional Example 3: Reading Solutions
on Graphs
Use the graph of the linear function to find
the value of y for the given value of x.
x=4
Start at the origin and
move 4 units right.
y
4
2
x
-4
-2
0
-2
-4
Course 1
2
4
Move up until you
reach the graph. Move
left to find the y-value
on the y-axis.
When x = 4, y = 2.
The ordered pair is (4, 2).
12-2 Graphing
Insert Lesson
Title Here
Functions
Try This: Example 3
Use the graph of the linear function to find
the value of y for the given value of x.
x=2
Start at the origin and
move 2 units right.
y
4
2
x
-4
-2
0
-2
-4
Course 1
2
4
Move up until you
reach the graph. Move
left to find the y-value
on the y-axis.
When x = 2, y = 4.
The ordered pair is (2, 4).
12-2 Graphing Functions
Additional Example 4: Graphing Linear
Functions
Graph the function described by the
equation. y = –x – 2
Make a function table.
Course 1
x
–x – 2
y
–1
–(–1) – 2
–1
0
–(0) – 2
–2
1
–(1) – 2
–3
Write these solutions as
ordered pairs.
(x, y)
(–1, –1)
(0, –2)
(1, –3)
12-2 Graphing
Insert Lesson
Title Here
Functions
Additional Example 4 Continued
Graph the ordered pairs on a coordinate plane.
y
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2
-1
-2
-3
-4
-5
Course 1
x
3 4 5
Draw a line through the
points to represent all the
values of x you could have
chosen and the
corresponding values of y.
12-2 Graphing Functions
Try This: Example 4
Graph the function described by the
equation. y = –x – 4
Make a function table.
x
–x – 4
y
–1
–(– 1) – 4
–3
0
–(0) – 4
–4
1
–(1) – 4
–5
Course 1
Write these solutions as
ordered pairs.
(x, y)
(–1, –3)
(0, –4)
(1, –5)
12-2 Graphing
Insert Lesson
Title Here
Functions
Try This: Example 4
Graph the ordered pairs on a coordinate plane.
y
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2
-1
-2
-3
-4
-5
Course 1
x
3 4 5
Draw a line through the
points to represent all the
values of x you could have
chosen and the
corresponding values of y.
12-2 Graphing
Insert Lesson
Functions
Title Here
Lesson Quiz
1. Use the given x-values to write solutions as
ordered pairs to the equation y = –3x + 1 for x =
0, 1, 2, and 3. (0, 1), (1, –2), (2, –5), (3, –8)
2. Determine whether (4, –2) is a solution to the
equation y = –5x + 3. No, –2 ≠ –5(4) + 3
3. Graph the function described by the equation
y = –x + 3.
Course 1