Investigate and Analyze cube root graphs

Investigate and Analyze cube root graphs

By Bette Horsington

Use the Center point x value for the decrease interval.

-∞ < x < -3, -3< x <∞

​

As x → -∞ the y → ∞ ​

​As x → ∞ the y → -∞

​​

​

​These are tips for the decreasing cube root graphs.

​Given the graph

(decreasing) ​

​

Multiple Choice

$$y=-\sqrt[3]{x-2}+3$$  , what is the domain and range?

• Domain x > 2

  Range y <3

• Domain All Reals

  Range y < 3

• Domain All Reals

  Range All Reals

• Domain x >2

  Range All Reals

Multiple Choice

$$y=-\sqrt[3]{x-2}+3$$  Is this function Increasing or Decreasing? What is the Interval?

• Increasing

  Interval All Reals

• Decreasing Interval All Reals

• Increasing

  $$-\infty<x<2,\ 2<x<\infty$$  

• Decreasing

  $$-\infty<x<2,\ 2<x<\infty$$  

Multiple Choice

$$y=-\sqrt[3]{x-2}+3$$  End Behavior

$$a.\ \ \ \ x\rightarrow-\infty\ \ then\ ;\ \ \ \ b.\ \ \ x\rightarrow\infty\ then\$$  

• $$a.\ \ y\ \rightarrow\ \infty$$  

  $$b.\ \ y\rightarrow-\infty$$  

• $$a.\ \ \ y\rightarrow-\infty$$  

  $$b.\ y\rightarrow\infty$$  

• $$a.\ \ x\rightarrow\infty$$  

  $$b.\ \ \ x\rightarrow-\infty$$  

• $$a.\ y\rightarrow2$$  

  $$b.\ \ y\rightarrow3$$  

Multiple Choice

$$y=-\sqrt[3]{x-2}+3$$  

a. x-intercept b. y-intercept

• $$a.\ \ none$$  

  $$b.\ \ \left(0,\ 4.26\right)$$  

• $$a.\ \ 4.26$$  

  b. $$4.26$$  

• $$a.\ \ \left(29,\ 0\right)$$  

  $$b.\ \left(0,\ 4.26\right)$$  

• $$a.\ \ 29$$  

  $$b.\ \ 4.26$$  

Multiple Choice

$$y=-\sqrt[3]{x-2}+3$$  If $$x=3\ find\ f\left(x\right)\$$  

• no solution

• 2

• 4

Multiple Select

$$y=-\sqrt[3]{x-2}+3$$ which of the following have none for it's answer? (choose all that apply!) 

• Maximum

• Minimum

• Horizontal Asymptote

• Vertical Asymptote

• Increase Interval

Use the Center point x value for the increase interval.

-∞ < x < -4, -4< x <∞

​

As x → -∞ the y → -∞ ​

​As x → ∞ the y → ∞

​​

​

​These are tips for the increasing cube root graphs.

​Given the graph

(increasing) ​

​

Multiple Choice

$$y=\sqrt[3]{x-2}-3$$  , what is the domain and range?

• Domain x > 2

  Range y >-3

• Domain All Reals

  Range y > -3

• Domain All Reals

  Range All Reals

• Domain x >2

  Range All Reals

Multiple Choice

$$y=\sqrt[3]{x-2}-3$$  , Is this function Increasing or Decreasing? What is the Interval?  

• Increasing Interval

  $$-\infty<x<\infty$$  

• Decreasing Interval $$-\infty<x<-3$$  

  $$-3<x<\infty$$  

• Increasing Interval

  $$-\infty<x<2$$  

  $$2<x<\infty$$  

• Decreasing Interval

  $$-\infty<x<\infty$$  

Multiple Choice

$$y=\sqrt[3]{x-2}-3$$  

a. x-intercept b. y-intercept

• $$a.\ \ 29$$  

  $$b.\ \ -4.26$$  

• $$a.\ \ \left(29,0\right)$$  

  $$b.\ \ \left(0,-4.26\right)\$$  

• $$a.\ \ \left(0,\ 29\right)\$$  

  $$b.\ \ \left(-4.26,0\right)\$$  

• a. none

  b. $$\left(0,-4.26\right)\$$  

Multiple Choice

$$y=\sqrt[3]{x-2}-3$$  , End Behavior

$$a.\ \ x\rightarrow\ -\infty\ \ \ \ \ \ \ \ \ \ \ \ \ \ b.\ \ x\rightarrow\ \infty$$  

• $$a.\ \ y\ \rightarrow-\infty\ \$$

  $$\ \ b.\ \ y\rightarrow\ \infty$$   

• $$\ \ a.\ \ y\rightarrow\ \infty$$  

  $$\ \ b.\ \ y\rightarrow\ -\infty$$  

• $$\ \ a.\ \ y\rightarrow\ -3$$

  $$\ \ b.\ \ y\rightarrow\ \infty$$   

• $$a.\ x\rightarrow-\infty$$  

  $$b.\ \ \ x\rightarrow\infty$$  

Poll

How are you feeling about Cube Root Graphs

• Great, this is easy

• Okay, I think I get it

• Confused, I am going to ask questions

• Huh? What's a cube root graph?