The equation of the graphed function is;
f(x) = -3/[(x + 3)(x - 2)]
- From the given graph, we see that the vertical assymptotes are at x = -3 and x = 2.
This means that at values of x = -3 or x = 2, the denominator becomes zero and the function becomes undefined.
- This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is;
(x + 3)(x - 2)
- Now,we see that the y-intercept is (0, 0.5). This means that when x = 0, y = 0.5.
- Let the numerator of the equation of the function be named a.
Thus, we have;
f(x) = a/((x + 3)(x - 2))
At (0, 0.5), we have;
0.5 = a/((0 + 3)(0 - 2))
0.5 = a/(-6)
Multiply both sides by -6 to get;
-3 = a
- Thus, the equation of the function is;
f(x) = -3/((x + 3)(x - 2))
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