Graphing a function

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kseel

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Can someone double check that I did this correct I don't think I did.

Sketch a graph with x=3 as a vertical asymptote, y=1 as a horizontal asymptote and x-intercepts 2 and 4.

Is x^2-6x+8/x^2-6x+9 right? If not what would it be I have been working on this for hours and I am stuck or missing something.

I got x^2-6x+8 because (x-2)(x-4).

Then x^2-6x+9 is because the vertical asymptote is y=1 it has to be x^2 and the vertical asymptote is x=3 so factored out it would be (x-3)^2 right? This is where my problem lays.
 
kseel said:
Can someone double check that I did this correct I don't think I did.

Sketch a graph with x=3 as a vertical asymptote, y=1 as a horizontal asymptote and x-intercepts 2 and 4.

Is x^2-6x+8/x^2-6x+9 right? If not what would it be I have been working on this for hours and I am stuck or missing something.

I got x^2-6x+8 because (x-2)(x-4).

Then x^2-6x+9 is because the vertical asymptote is y=1 it has to be x^2 and the vertical asymptote is x=3 so factored out it would be (x-3)^2 right? This is where my problem lays.
Click to expand...

You need to use grouping symbols/parentheses: f(x) = (x^2-6x+8)/(x^2-6x+9)

Why do you doubt your work? Have you tried graphing it on a graphing calculator? Or tried Googling graph y=(x^2-6x+8)/(x^2-6x+9) ?
 
kseel said:
Can someone double check that I did this correct I don't think I did.

Sketch a graph with x=3 as a vertical asymptote, y=1 as a horizontal asymptote and x-intercepts 2 and 4.

Is x^2-6x+8/x^2-6x+9 right? If not what would it be I have been working on this for hours and I am stuck or missing something.

I got x^2-6x+8 because (x-2)(x-4).

Then x^2-6x+9 is because the vertical asymptote is y=1 it has to be x^2 and the vertical asymptote is x=3 so factored out it would be (x-3)^2 right? This is where my problem lays.
Click to expand...

Possibly you were simply to draw a graph with the given characteristics (don't bother about finding a formula for a function with the properties), thus showing that you know what asymptotes and roots look like. However, the function you give DOES have the desired roots and asymptotes. Since you chose a quadratic numerator and need a horizontal asymptote, you need a quadratic denominator as well, and since you need a single asymptote, the denominator has to have a double root (be a square). So your formula is fine. However, sketching its graph is another task. If you primarily need the sketch, then you have a ways to go.
 
girodd said:

Possibly you were simply to draw a graph with the given characteristics (don't bother about finding a formula for a function with the properties), thus showing that you know what asymptotes and roots look like. However, the function you give DOES have the desired roots and asymptotes. Since you chose a quadratic numerator and need a horizontal asymptote, you need a quadratic denominator as well, and since you need a single asymptote, the denominator has to have a double root (be a square). So your formula is fine. However, sketching its graph is another task. If you primarily need the sketch, then you have a ways to go.
Click to expand...

I can sketch it I just wanted to make sure I had it right before I did as it just didn't look right to me. Thanks to you both.
 
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