SOLUTION: rewrite the function in simplify form and find order pair associated where the hole is 2 5x - 10x/5x five x square minus ten x over five x

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Question 230517: rewrite the function in simplify form and find order pair associated where the hole is
2
5x - 10x/5x five x square minus ten x over five x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%285x%5E2+-10x%29%2F%285x%29
To simplify this or any fraction, you cancel common factors. And to cancel common factors we must have factors. So we start by factoring. The Greatest Common Factor (GCF) of the numerator is 5x. (The denominator is already a product.):
f%28x%29+=+%285x%28x+-+2%29%29%2F%285x%29
Now we can cancel the common factors, as long as the factors are not zero! So the 5x's will cancel only if x is not zero!
f%28x%29+=+%28cross%285x%29%28x+-+2%29%29%2Fcross%285x%29
leaving:
f%28x%29+=+x-2 as long as x is not zero.

In general a hole in the graph will occur for any x value that would make any of the canceled factors zero. In this case the hole occurs when x = 0. And we can use our simplified f(x) to find the y for x=0:
f%280%29+=+%280%29-2+=+-2

So the graph of f%28x%29+=+%285x%5E2+-10x%29%2F%285x%29 will be the same as the graph of f(x) = x-2 (a straight line with slope of 1 and y-intercept of -2) except there will be a hole at (0, -2).