SOLUTION: f(x) = x^3 − 2x^2 − 4x + 8 / x − 2 Find any hole(s) in the graph of f. Find the zero(s) of f. On what interval(s) is f(x) > 0? On what interval(s) is f(x)

SOLUTION: f(x) = x^3 − 2x^2 − 4x + 8 / x − 2 Find any hole(s) in the graph of f. Find the zero(s) of f. On what interval(s) is f(x) > 0? On what interval(s) is f(x) < 0?

Question 1113885: f(x) = x^3 − 2x^2 − 4x + 8 / x − 2
Find any hole(s) in the graph of f.
Find the zero(s) of f.
On what interval(s) is f(x) > 0? On what interval(s) is f(x) < 0? (Using interval notation)
Find the interval(s) on which f is increasing or decreasing. (Using interval notation)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

as long as x-2 is not 0.

So the given function is the same as the function x^2-4 except at x=2, where the given function is undefined.

So there is a hole in the graph of the given function at x=2. At x=2, the value of the function x^2-4 is 0, so the hole in the graph of the given function is at (2,0).

The zeros of the given function are the zeros of x^2-4, which are 2 and -2.

The graph of x^2-4 is a parabola opening upward; the function value is negative between the two zeros of the function and positive "outside" the zeros:
positive on (-infinity, -2) and (2, infinity);
negative on (-2,2).

The vertex of x^2-4 is at (0,-4); the function is decreasing on (-infinity, 0) and increasing on (0, infinity).
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SOLUTION: f(x) = x^3 &#8722; 2x^2 &#8722; 4x + 8 / x &#8722; 2 Find any hole(s) in the graph of f. Find the zero(s) of f. On what interval(s) is f(x) > 0? On what interval(s) is f(x) < 0?

SOLUTION: f(x) = x^3 − 2x^2 − 4x + 8 / x − 2 Find any hole(s) in the graph of f. Find the zero(s) of f. On what interval(s) is f(x) > 0? On what interval(s) is f(x) < 0?