Question 1128232: Use a calculator to graph f(x). Use the graph to solve f(x) > 0. (Enter your answer using interval notation.)
f(x) = x + 5/ (x − 2)(x − 4)
f(x) > 0 when x is in
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If the problem tells you to use your calculator to graph the function, then we can't do it for you....
By the way, make sure you enter the function correctly, with parentheses where required: f(x) = (x+5)/((x-2)(x-4)), or
The graph you get should show vertical asymptotes at x=2 and x=4, because either of those values makes the denominator 0 and so the function is not defined. And it should show you a single zero at x=-5, because that is the only value of x that makes the numerator 0.
Then you can find where the function value is positive by looking at the factors in the expression:
(-infinity, -5): all three factors negative, so function value negative
(-5,2): two factors negative, so function value positive
(2,4): one factor negative, so function value negative
(4,infinity): no factors negative; so function value positive
So the graph you get should show the function value greater than 0 for x values between -5 and 2, and for x values greater than 4.
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