Describe the discontinuities of f(x)=x^2+x-6/x^2-5x+6. Find an equivalent form for f that shows how the graph of f is related to the graph of y=1/x. Describe the relationship.

Question

angelwings996 · Answer

$$f(x)=\frac{ x ^{2}+x-6 }{ x ^{2}-5x+6 }$$

anonymous · Answer

soo for discontinuities you would find the values in the denominator that make x zero... so factor it.

angelwings996 · Answer

Well I got x=0 for that part

anonymous · Answer

(x-3) (x-2) ?

anonymous · Answer

and then (x-2)(x+3) for the numerator

angelwings996 · Answer

Oh sorry, I wasn't sure what to do, do I factor both denominator and numerator?

anonymous · Answer

I'm pretty sure. to find where the graph discontinues.

angelwings996 · Answer

Okay, so after factoring, what do I do?

anonymous · Answer

What discontinuity implies is when there isnt a value where there is an answer for x and y, and since you cant divide by zero, anytime the numerator can be zero, it discontinues.

angelwings996 · Answer

Okay I see what your saying

angelwings996 · Answer

So would I then cancel out x-2 because it is on the bottom and top ?

anonymous · Answer

Yeah exactly.

anonymous · Answer

So then for the second part of the question, how does it relate to y=1/x, you know that when x is zero in that case it cannot have a value. so the graph becomes a hyperbola.

angelwings996 · Answer

Alright, I get you so far

anonymous · Answer

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