SOLUTION: Given the function, f(x)= 2/x^2-2x-3 find tthe domain and range by showing your work. After that, find the x and y intercepts

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given the function, f(x)= 2/x^2-2x-3 find tthe domain and range by showing your work. After that, find the x and y intercepts      Log On


   

Question 1012572: Given the function, f(x)= 2/x^2-2x-3 find tthe domain and range by showing your work. After that, find the x and y intercepts
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2%2F%28x%5E2-2x-3%29=2%2F%28%28x%2B1%29%28x-3%29%29
There are only two restrictions on x that make the denominator go to zero.
So x=-1 and x=3 are excluded from the domain.
Domain : (-infinity,-1)U(-13)U(3infinity)
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We can plot to look for the range,
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So from the graph, you see that as you move from left to right you go from 0 to infinity, -infinity to -1%2F2, and then from infinity back to 0.
So the range is,
Range: (-infinity,-1%2F2]U(0infinity)
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There is no x-intercept, the graph never crosses the x-axis.
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When x=0,
y=2%2F%28-3%29=-%282%2F3%29
So the y-intercept is
(0,-2%2F3)