Meera practice 2

End Behavior Review

11/10/20

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

• $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

•  $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$   $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$ 

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

•  $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$   $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$ 

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

•  $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$   $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$ 

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

•  $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$   $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$ 

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

Multiple Choice

What is the end behavior of this function?

• 
  

  $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$
  

• $As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

•  $\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$   $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$ 

• $As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

End Behavior

​

If the leading coefficient is positive then the graph will always end up

​

If the leading coefficient is negative the graph will always end going down.

​

Multiple Choice

what the is the end behavior

• Up, up

• up, down

• down, down

• down, up

Multiple Choice

what the is the end behavior

• Up, up

• up, down

• down, down

• down, up

Multiple Choice

what the is the end behavior

• Up, up

• up, down

• down, down

• down, up

Multiple Choice

what the leading coefficient

• Postive

• Negative

• Even

• Odd

Multiple Choice

what the is the degree of the polynomial

• Postive

• Negative

• Even

• Odd

Multiple Choice

what the is the Leading Coeffiecent and Degree

• Positive, Odd

• Negative, Odd

• Postive, Even

• Negative, Even

Multiple Choice

what the is the leading coefficient and degree

• Postive, Odd

• Negative, Odd

• Postive, Even

• Negative, Even

Multiple Choice

What does x tell us 

• Left and right
• Up and down

Multiple Choice

What does y tell us 

• Left and right
• Up and down

Multiple Choice

Which one means left

• x →-∞
• x →∞

Multiple Choice

Which one means up

• y →-∞
• y →∞

Multiple Choice

Which one means the function goes up on the left

• x →-∞, y→∞
• x →-∞, y→-∞

Multiple Choice

Which one means the function goes down on the left

• x →-∞, y→∞
• x →-∞, y→-∞

Multiple Choice

What is the End behavior on the left side

• x →-∞, y→∞
• x →∞, y→-∞
• x →-∞, y→-∞
• x →∞, y→∞

Multiple Choice

What is the End behavior on the left side

• x →-∞, y→∞
• x →-∞, y→-∞
• x →∞, y→∞
• x →∞, y→∞

Multiple Choice

What is the End behavior on the right side

• x →-∞, y→∞
• x →-∞, y→-∞
• x →∞, y→∞
• x →∞, y→-∞

Multiple Choice

What is the end behavior on the left side

• x →∞, y→∞
• x →-∞, y→-∞
• x →-∞, y→∞
• x →∞, y→∞

Multiple Choice

What is the End behavior on the right side

•  x→∞, y→∞
•  x→⁻∞, y→∞
•  x→⁻∞, y→0
•  x→∞, y→⁻∞

Multiple Choice

What is the End behavior on the left side

•  x→∞, y→∞
•  x→⁻∞, y→∞
•  x→⁻∞, y→0
•  x→∞, y→⁻∞

Multiple Choice

What is the end behavior of the function

•  x →∞, y→∞ and x→∞, y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
•  x →∞, y→∞ and x→⁻∞, y→0
•  x →∞,y→∞and x→⁻∞, y→⁻∞

Multiple Choice

What is the end behavior of the function

•  x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
•  x →∞, y→∞ and x→⁻∞, y→0
• x →∞,y→∞ and x→⁻∞, y→⁻∞

Multiple Choice

What is the end behavior of the function

•  x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
• x →∞, y→∞ and x→⁻∞, y→2
•  x →∞,y→2 and x→⁻∞, y→∞

Use the chart to complete your notes for Summary of Graphing Parent Functions.​

​

Polynomials - Graphing

End Behavior

​Notation

​

Domain and range

​

Domain

Range

To find the domain, look at which possible x-values there are

On this graph, x can be any number that is greater than -5, so the domain is x>=-5

To find the range, find which y-values are possible

On this graph, y can be any number less than or equal to 5 so the range is y<=5

2 more examples of domain and range

When there is a white dot, that value is not included, a black dot is included

On this graph, that means -3 is not included but the value of 1 is so the domain is -3

Multiple Choice

Is 5 a possible x-value for this function?

• yes

• no

Multiple Choice

Is 0 a possible x-value for this function?

• yes

• no

Multiple Choice

Is 2 a possible x-value for this function?

• yes

• no, because a white dot is an excluded value

• no, because a black dot is an excluded value

Multiple Choice

Is -3 a possible x-value for this function?

• no

• yes, because a white dot is an excluded value

• yes, because a black dot is an included value

Multiple Choice

What is the range of this graph

• -5<=y<=4

• 4<y<5

• -3<y<2

​

Multiple Choice

Is -1 a possible x-value?

• Yes

• No

Multiple Choice

Is 0 a possible x-value?

• Yes

• No

Multiple Choice

True or False: Since there is a white dot on 8, x can be equal to 8?

• True

• False

Multiple Choice

What is the domain of this function

• x>=-5

• -5<x<5

• y<=-5

Multiple Choice

What is the range of this function

• -5<=x<=5

• -5<x<5

• y>=5

• y<=5

Multiple Choice

What is the domain?

• {0, 1, 2, 15}

• (0, 1, 2, 3}

• {3, 7, 11, 15}

• {3, 7, 11, 3}

Multiple Choice

What is the range?

• -4 < x ≤ 5

• -4 ≤ x < 5

• -3 < y < 3

• -3 ≤ y ≤ 3

Multiple Choice

What is the Range?

• y ≥ 6
• y ≤ 6
• -10 ≤ y ≤ 6
• -10 ≤ x ≤ 6

Composite Functions Review

Alice Pham P.2

What is a composite function?

• Can be thought of a series of operations

• One function is substituted into another function

• Often denoted as f(g(x)) or (f ∘ g)(x)

• Read as "f of g of x"

Example

Multiple Choice

Identify if the following is a composite function:
 $f\left(x\right)\cdot g\left(x\right)$  

• Yes

• No

• It is an operation on functions

• You are multiplying f(x) and g(x) not substituting functions

Multiple Choice

Which expression represents g(f(x)) if

f(x) = 2x - 8 and

g(x) = 4x

• 8x - 32

• 8x² - 32x

• 8x - 8

• 6x - 8

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

• 16
• 4
• -4
• None of these.

Multiple Choice

• 136
• 4
• 8
• 147

Multiple Choice

What is f(g(3))?

• 1/8

• 8

• 1/4

• 1/2

Multiple Choice

Find f(h(5)) based on the graphs of f(x) and h(x)

• -6

• -3

• 6

• 2

Multiple Choice

• 9 - √17
• 4
• 2
• √8

Multiple Choice

Are $\tan x^2$ and  $\left(\tan x\right)^2$  the same thing?

• Yes

• No

Multiple Choice

• 8
• 3
• 2
• 0

Fill in the Blanks

Multiple Choice

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

• 9x² - 6x + 1

• 3x - 1

• 3x² - 1

• 9x² - 1

Multiple Choice

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

• g(f(x))= -6x²+31
• g(f(x))= -6x²+24
• g(f(x))=18x²-84x+90
• g(f(x))=9x²-42x-41

Fill in the Blanks

Multiple Choice

(L3) Given f(x)= x² + 25 and g(x)= x - 5, find     (f+g)(x). 

• x² + x - 20
• x² + x + 20
• -x² + x - 20
• x² - x - 20

Multiple Choice

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of g(f(-2)).

• -14
• 20
• 6
• 7

Fill in the Blanks

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

• -42
• -26
• -18
• None of these.

Composite Functions Lessons

Elizabeth Borres

At the end of the lesson, students will be able to:

• Define composite functions.

• Solve composite functions.

• Apply composite functions in real life.

Let us have a short review.

(Function Operations)

Multiple Choice

If  $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then  $\left(f+g\right)\left(0\right)=$ 

•  $-1$  

•  $3$  

•  $1$  

•  $-3$  

Multiple Choice

If  $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then  $\left(f-g\right)\left(1\right)=$ 

• 3

• -3

• 1

• -1

Multiple Choice

If  $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then  $\left(f\cdot g\right)\left(-1\right)=$ 

• -3

• -14

• 14

• -7

Multiple Choice

If  $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then  $\left(\frac{f}{g}\right)\left(\frac{2}{5}\right)$ 

• undefined

•  $\frac{1}{3}$  
  

•  $\frac{-1}{3}$  

•  $-3$  

Poll

Any question(s)?

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

• 16
• 4
• -4
• None of these.

Multiple Choice

f(x) = 3x + 10

g(x) = x - 2

Find g(f(-10))

• -42

• -26

• -18

• None of these.