Aquariums, Stands and Canopies Review September 27 th, 2012.
September 27 th
description
Transcript of September 27 th
September 27th
Please Complete Warm Up
1. Find (g•f) G(x)=3x² and f(x)=2x-5
2. Find Slope (5, -6) and (2,3)
Warm-Up
Thursday, October 3rd
Homework Answers
Think, Pair, share
Combining Functions
Writing FuctionsLet f(x)=4x+3 and
g(x)=2x+5
f(x) - g(x)Also written
(f g)(x)
f(g(x))Also written
(f g)(x)
Real-Life applicationThe volume V of a cube with edge length s is given by the function V(s) = s3. Find V(4).
Explain what V(4) represents.
Identifying aLinear Function
by Its Graph
In a linear function, a _________ change in x corresponds to a ___________ change in y.
Identifying a Linear Function by it’s Table
What should you NOT find in a linear
Equation?1. 2.3.4.5.
Do you Remember?
Function Graphic Organizer
Part I: Intercepts
What is an INTERCEPT?
When you hear the word intercept what do you think of
?
I. X and Y intercept Definitions
X intercept
•The x coordinate where the graph intersects the x axis.
•Y coordinate is ALWAYS 0
•Example: (3,0)
Y intercept
•The y coordinate where the graph intersects the y axis
•X coordinate is always 0
•Example: (0,3)
X and Y InterceptsUsing Graphs
•What is the x- intercept?•What is the y-intercept?•How do you know
You Try!
Question of the Day
•If I know that x is always 0 for the y intercept, how could I find it?
•If I know that y is always 0 for the x intercept, how could I find it?
2X-3Y=20
5x – 2y = 10
5x – 2y = 105x – 2(0) = 10
5x – 0 = 105x = 10
To find the y-intercept, replace x with 0 and solve for y. Why can we replace with 0?
To find the x-intercept, replace y with 0 and solve for x. Why can we replace with 0?
x = 2The x-intercept is 2.
5x – 2y = 105(0) – 2y = 10
0 – 2y = 10 – 2y = 10
y = –5The y-intercept is –5.
Find the x- and y-intercepts.
#1
“Cover upMethod”
Finding Interceptsin an equation
Finding Interceptsin an equation
5x – 2y = 10
5x – 2y = 105x – 2(0) = 10
5x – 0 = 105x = 10
x = 2The x-intercept is 2.
5x – 2y = 105(0) – 2y = 10
0 – 2y = 10 – 2y = 10
y = –5The y-intercept is –5.
Find the x- and y-intercepts.
“Cover up”
#2 2x – 3y = 12 X intercept
Cover up the y and solve2x-3y=12
2x=12x=6
(6,0)
Y intercept
Cover up the x and solve
2x-3y=12-3y=12
y=-4(0,-4)
#3 Find the x- and y-intercepts.
–3x + 5y = 30–3x + 5y = 30
–3x + 5(0) = 30
–3x – 0 = 30–3x = 30
x = –10The x-intercept is –10.
–3x + 5y = 30–3(0) + 5y = 30
0 + 5y = 30 5y = 30
y = 6The y-intercept is 6.
#4Find the x- and y-intercepts.
4x + 2y = 16 4x + 2y = 16
4x + 2(0) = 16
4x + 0 = 16 4x = 16
x = 4
The x-intercept is 4.
4x + 2y = 164(0) + 2y = 16
0 + 2y = 16 2y = 16
y = 8
The y-intercept is 8.
Graphing Linear Equations by Using Intercepts
Use intercepts to graph the line described by the
equation.3x – 7y = 21Step 1 Find the intercepts.
x-intercept: y-intercept:3x – 7y = 21
3x – 7(0) = 213x = 21
x = 7
3x – 7y = 21
3(0) – 7y = 21–7y = 21
y = –3
Step 2: Place intercepts on a graph and connect
x
Final Product
Part 2: Slope and Rate of Change
Slope When you think of the
word SLOPE…what do you think
of?!
Slopes are commonly associated with mountains
The slope we are studying is associated with the graph of a line
Different Slopes Po
sitive
Negativezero
Undefined
POSITIVE SLOPE“Reaching the Goal”
Negative Slope“The Tumbler”
Zero Slope“Not Much Happening”
Horizontal Line
Undefined Slope“Only Spider Man”
Slope Horizontal vs. Vertical
Horizontal: 0Verical: Undefined
EquationsHorizontal vs. Vertical
Horizontal: y=no xVerical: x=no y
How do we find slope Using Graphs?!?!
I. Rise and Run
Rise= y axis
Run= x axis
What goes first?You need to
rise up before you
run
Finding Slope with a GraphFind the slope of the line
Begin at one point and count vertically to fine the rise.
• Up=Positive • Down=NegativeThen count horizontally to the
second point to find the run.• Right=Positive • Left= Negative
It does not matter which point you start with. The slope is the same.
(3, 2)
(–6, 5)
•
•
Rise 3
Run –9
Rise –3
Run 9
YOU TRYFind the slope of the line
Begin at one point and count vertically to find rise.
Remember: up=____ down=___
•
•
Then count horizontally to the second point to find the run
Remember: right=____left=_____
Rise 2
Run –5
Rise –2
Run 5
Slope in a Table
Rate of Change
•When you hear the phrase: Rate of Change
What do you think of?!??!
A rate of change is change in x over the change in Y
OR
The table shows the average Winter temperature (°F) for five months in Suwanee. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?
Y Xdependent: temperature independent: month
Remember!!!!!ALWAYS y
x
Find the rates of change for all 4 Intervals
When was the greatest rate of change?!?!
3 to 5
5 to 7
7 to 8
2 to 3
The Slope Formula
2 1
2 1
y yrisesloperun x x
1st Ordered Pair (x1, y1) and 2nd Ordered Pair (x2, y2)
The letter ‘m’ is used to identify slope.
Example #1: (3,4) (5,6)
#2 Find the slope of the line that contains
(2, 5) and (8, 1)
Use the slope formula.
Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2).
Simplify.
Find the slope of the line that contains (5, –7) and (6, –4)
#3
Use the slope formula.Substitute (5, –7) for (x1, y1) and (6, –4)
for (x2, y2).
Simplify.
m=3= 3
Find the slope of the line that contains (–2, –2) and (7, –2)
You TRY!!!
Use the slope formula.
Substitute (–2, –2) for (x1, y1) and (7, –2) for (x2, y2).
SimplifyM= 0How could I just look at the points and KNOW the slope is going to be 0?
= 0
Review
1. 2.
3. (3, 4) (1, 2) 4. (-1, -3) (6, 7)
5. (9, -4) (-3, -2)
Describe Slope Describe Slope