#1 GRFP

#1 Graphing Rational Functions Practice

By Krystal Hill

Multiple Choice

First we are going to find the vertical asymptote(s) of the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  . What do I calculate to determine the vertical asymptote(s)?

• Zeros of the numerator

• Zeros of the denominator

• Degrees of both the numerator and denominator

• There is no way to do this.

To find the vertical asymptotes, you will factor the denominator.

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Please factor now, showing work on your paper.

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If you need help, the next slide has a video.

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Once done, move to the next slide.​

Multiple Select

What are the vertical asymptotes you get for the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  ?

• x=4

• x=-4

• x=1

• x=-1

• x=-2

Multiple Choice

Now we are going to find the horizontal asymptote of the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  . What do I calculate to determine the horizontal asymptote?

• Zeros of the numerator

• Zeros of the denominator

• Degrees of both the numerator and denominator

• There is no way to do this.

Now find the horizontal asymptote, showing work on your paper.

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If you need help, the next slide has a video.

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Once done, move to the next slide.​

Multiple Choice

What is the horizontal asymptotes you get for the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  ?

• y=0

• No HA

• y=1

• x=1/4

Multiple Choice

Next is to find the x-intercepts of the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  . What do I calculate to determine the x-intercepts?

• Zeros of the numerator

• Zeros of the denominator

• Degrees of both the numerator and denominator

• There is no way to do this.

To find the x-intercepts, you will factor the numerator.

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Please factor now, showing work on your paper.

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If you need help, the next slide has a video.

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Once done, move to the next slide.​

Multiple Select

What are the x-intercepts you get for the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  ?

• -3

• 3

• 0

• -2

• 2

Recall, that a hole will occur IF:

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The same number shows up as a vertical asymptote AND a x-intercept.

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Determine if we have a hole in the graph.​

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Once done, move to the next slide.​

Fill in the Blanks

Is there a hole in the graph of the function $f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$  ?

Multiple Select

Next we create a signline so we can determine where the graph will be above or below the x-axis.  What numbers do I use to create the signline?

• VA's

• x-intercepts

• HA's

• holes

Now, we create a signline using the VA's and the x-intercepts.

The video has an error. The first space in your signline should be negative.

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Please do so now, showing work on your paper.​

If you need help, the next slide has a video.​

Once done, move to the next slide.​

Finally we create a rough sketch of the graph.

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Please do so now, on your paper.

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Once done, move to the next slide.​

Poll

How confident are you that you created a correct sketch of the graph of the function $$f\left(x\right)=\frac{x^3+x^2-6x}{4x^2+4x-8}$$  ?

• I think I graphed it wrong

• I am not very confident, but I think I graphed it mostly correct

• I am not very confident, but I think I graphed it all correct

• I am very confident that I graphed it all correct