f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.
<h3>Write an equation for the function:</h3>
Let where P(X) and Q(X) are polynomial function.
The function has the following:
- From the given graph, we can say that the vertical asymptotes x = - 2 and x = 3, 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:
⇒ Q(X) = (x + 2)(x - 3)
- From the given graph, we can say that the zero is 3, P(X) has the factor (x - 3)
Let a be the leading coefficient of P(X)
⇒ P(X) = a(x - 1)
Now for finding the value of a we can rewrite the equation as,
⇒ f(x) = P(X)/Q(X)
⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]
⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]
Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2
⇒ - 2 = -a/[(2)(- 3)]
⇒ a = - 2 × 2 × 3
⇒ a = - 12
By putting a = -12 in f(x) we get,
⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]
Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.
Learn more about graphed functions here:
brainly.com/question/24886387
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