Algebra

Unit 3

Summer

Monday July 19, 2021 Activator

+X

+Y

-X

-Y

Where is (3, 5)? +3 right and +5 up

What does the 3 mean? Right

What does the 5 mean? Up

Is x the number line? Yes

New Seats

Page #3 Lesson 3.1

Today’s Objective

Students will be able to graph lots of points in function notation.

Lesson 3.1

Today’s New Vocab (1 of 4)Graph and connect the points in the following sequence.(-2,1) (2left, 1up)(2,-3) (2right, 3down)(2, 2) (2right, 2up)(-2,-3) (2left, 3down)(4, 0) (4right, 0up)(-2,1) (2left, 1up)

https://www.youtube.com/watch?v=r16I6LB2YbQ 0:30-2:30 and 4:15-6:15

A

C

BD

E

Today’s New Vocab (2 of 4)Write the points in function notation.

f(0) =

G(3) =

H(6)=

5

3

1

(0, 5)

(3, 3)

(6, 1)

G

H

Today’s New Vocab (3 of 4)

F(7) = -5

Write the function as a point.Graph the point.

(7, -5)

B(-4) = 6 (-4, 6)What point is this? F

What point is this? B

Right

Left

Down

UP

Today’s New Vocab (4 of 4)

G(x) = -2x F(x) = x - 7 What is G(3) and F(4)?

G(3) = -2(3) G(3) = -6 (3, -6)

F(4) = (4) - 7 F(4) = -3

(4, -3)The point is...

Group Work Questions

#1#2#3#4#5

#6#7#8#9#10

13, 3, 4, 10

17, 7, 8, 12

16, 5, 6, 11

13, 3, 4, 10

13, 3, 4, 10

13, 3, 4, 1016, 5, 6, 11

16, 5, 6, 11

17, 7, 8, 12

17, 7, 8, 12

Page #1 Lesson 3.1

.

Monday July 19, 2021 Work PeriodGraph the points and write the functions.

(x, y)(-4, 4)(-2, 2)(0, 0)(2, -2)

X

y

F(-4) = 4

G(-2) = 2

H(0) = 0J(2) = -2

y = -x

Page #4 Lesson 3.1

Monday July 19, 2021 Exit Ticket

.

Graph the table and write the functions.

X Y

-3 -6

-2 -4

1 2

2 4

X

y

F(-3) = -6G(-2) = -4H(1) = 2

J(2) = 4

Make a table for this function.

X(input) f(x) (output)

-1 10

0 3

3 -6

4 -5

5 -2

Tuesday July 20, 2021 Activator

Right and Left Up and Down

Page #7Lesson 3.2

Today’s Objective

Students will be able to determine if problems are functions.

Lesson 3.2

Today’s New Vocab (1 of 4)Can the calculator make a table for you?

f(x) = 3x X Y

-1 -3

0 0

1 3

2 6

Today’s New Vocab (2 of 4)

x (input) f(x) = 3x f(x) or y

f(-1) f(-1) = 3( -1 ) -3f(0) f(0) = 3( 0 ) 0f(1) f(1) = 3( 1 ) 3f(2) f(2) = 3( 2 ) 6

f(x) = 3x is a line on a graph.

If every point is f, then the line is called f.

Today’s New Vocab (3 of 4)

X f(x) or y

-2 -6

-1 -3

0 0

1 3

2 6

f(x)= 3xMake a table and graph

Is this a point or line at F(-4)? a pointF(x) = 3x F(-4) = -12

F(-4) = 3(-4) F(-4) = -12

F(x) is a line called F or F(x).

F(-4) is a point called F

(-4, -12)

Today’s New Vocab (4 of 4)

Group Work Q’s Skip 2C,3A,3B

#1#2#3#4#5

#6#7#8#9#10

5BC,7BC, 1AB,2D

5DE,7DE,1AB,2D

5CD,7FG, 1AB,2D

5BC,7BC, 1AB,2D

5BC,7BC, 1AB,2D

5BC,7BC,1AB,2D5DE,7DE,1AB,2D

5DE,7DE,1AB,2D

5BC,7BC, 1AB,2D

5BC,7BC, 1AB,2D

Page #6Lesson 3.2

Tuesday July 20, 2021 Work Period

.

f(x) = 2x g(x) = x + 2

What is f(3) + g(3) ? 6 + 5 is 11

What is f(3)(g(3)) ? 6(5) is 30

What is f(3) - g(3) ? 6 – 5 is 1

f(3) = 2(3) g(3) = (3) + 2

f(3) = ___ g(3) = ____ 6 5

Evaluate when g(3) and f(3). Page #8Lesson 3.2

Tuesday July 20, 2021 Exit Ticket

.

Make a table from the graph.

A

B

C

D

X f(x)

0 3

2 2

4 1

6 0What is f(4)? 1

What is f(0)? 3

Wednesday July 21, 2021 Activator Enter the function.Make a table. g(x) = x - 7

X G(x)

0 -7

1 -6

2 -5

3 -4

4 -3

5 -2

Page #11Lesson 3.3

Describe this line. Subtract 7

Today’s Objective

Students will be able graph a function and determine if it is a function.

Lesson 3.3

Today’s New Vocab (1 of 4)

X G(x)

0 -7

1 -6

2 -5

3 -4

4 -3

g(x) = x−𝟕Graph the function.

What is g(1)? -6

What is this point?

(1,-6)

Today’s New Vocab (2 of 4)Evaluate the function for g(2) and g(4)

g(x) = x - 7

g(2) = (2) - 7

g(2) = 2 - 7 g(2) = -5

g(x) = x - 7

g(4) = (4) - 7

g(4) = 4 - 7g(4) = -3

What number was next to 4 on the table? -3

Today’s New Vocab (3 of 4)What is a function? A function is an equationwhich gives a unique outputfor all inputs. Does something.

Is f(x) = x – 7 a function? Yes

X (input) Y (output)

0 -7

Today’s New Vocab (4 of 4)This graph is f(x) = 𝑥2

What is f(-2)? 4

What is f(-1)? 1

What is f(0)? 0

Write the point. (-2,4)

Write the point. (-1,1)

Write the point. (0,0)

A

B

C

D

E

Group Work Questions

#1#2#3#4#5

#6#7#8#9#10

1,3B,7AC,5D

1,3D,7AC,5C

1,3C,7BD,5B

1,3B,7BD,5D

1,3C,7AC,5B

1,3B,7AC,5D

1,3D,7BD,5C

1,3C,7BD,5B

1,3D,7AC,5C1,3B,7BD,5D

Page #9Lesson 3.3

Wednesday July 21, 2021 WP

.

Is this diagram a function? NoWhy? x=2 has two y-values.

Page #12Lesson 3.3

X Y

2 20

2 40

3 30

4 40

Repeat x = 2

Wednesday July 21, 2021 Exit Ticket

.

Translate the function into points, a table, and a graph.

f(-2) = 0f(-1) = 1

f(0) = 2

f(-3) = -1 (-3,-1) (-2,0) (-1,1) (0, 2)

X f(x)

-3 -1

-2 0

-1 1

0 2

f(x) = x+2

Thursday July 22, 2021 Activator

What is the maximum(or top) of the parabola

(or curved line) f(x)?State the point. ( 2, 1 )

What is f(4)? -3

B

A C

Page #15Lesson 3.4

Today’s Objective

Students will be able to determine the maximum and

minimum of a function.

Lesson 3.4

Today’s New Vocab (1 of 4)Make a table for the function f(x) = 𝒙𝟐 − 𝟒

Where is the exponent button?

X Y

-3 5

-2 0

0 -4

2 0

3 5

Today’s New Vocab (2 of 4)

X (Input) f(x) = 𝒙𝟐 − 𝟒 Y (output)

-3 (−𝟑)𝟐−𝟒 5

0 (𝟎)𝟐−𝟒 -4

3 (𝟑)𝟐−𝟒 5

What is f(-3)? 5 What is f(0)? -4What is f(3)? 5

How is the table calculated?

Today’s New Vocab (3 of 4)

X Y

-3 5

-2 0

0 -4

2 0

3 5

f(x)= 𝒙𝟐 − 𝟒Graph the function.

Where is the minimum or

(bottom)?

(0,-4)

Smallest y-value

Today’s New Vocab (4 of 4)Is f(x) = 𝒙𝟐 − 𝟒 a function? YES

Why?

Every x-value has exactly one answer when you substitute.

What is f(-5)?f(-5) = (−5)2−4

f(-5) = +25 −4

f(-5) = 21For example,

f(-5) = (-5)(-5) −4

Group Work Questions

#1#2#3#4#5

#6#7#8#9#10

1A, 3A, 3B

4A, 4B , 4C

1B, 2A, 2B

1A, 3A, 3B

1B, 2A, 2B

1A, 3A, 3B

4A, 4B , 4C

1B, 2A, 2B

4A, 4B , 4C1A, 2A, 2B

Page #13Lesson 3.4

Thursday July 22, 2021 Work Period

.

X G(x)

0 -6

1 -4

2 -2

3 0

Make a table for the function G(x) = 2x - 6

For what x-value does G(x) = 0 ? x = 3

What is G(3)?

G(3) = 6 - 6G(3) = 2(3) - 6

G(3) = 0 Page #16Lesson 3.4

C

A

Thursday July 22, 2021 Exit Ticket

.

For what value of

x does f(x) = 2? (-2,2)

For what value of

x does G(x) = 0? (3,0)

X

X

B

For what x-value does f(x) = G(x)? (1,-4)

X Intersection (solution)

Test 3 InfoFriday July 23, 2021

#9-10 are worth double points.No work needed on #6.All other questions must have work.

Test 3 InfoMonday July 26, 2021

#9-10 are worth double points.No work needed on #6.All other questions must have work.