SOLUTION: Find the domain of the function algebraically and write it using interval notation: f(x)=x/(x^2-7x)

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Question 912238: Find the domain of the function algebraically and write it using interval notation: f(x)=x/(x^2-7x)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x/(x^2-7x)
f(x)=x/(x(x-7))
Critical x values are 0 and 7.

No vertical root for x at zero because x is both in the numerator AND the denominator.
f is undefined and discontinuous for x at 0.

Vertical asymptote at x=7 because undefined for x at 7.

Intervals of x<0, 0 Near x=0, f becomes increasingly negative from either direction. (?)

Within 0 f=(+)/((+)(-))
f is negative

Within 7 f=(+)/((+)(+))
f is positive

That analysis is not really complete, but this should be the graph:

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F%28x%5E2-7x%29%29