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