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Consider the function below. f(x)= x² +3−x

(a) Find the vertical asymptote(s).
x=_______ Find the horizontal asymptote(s).
y=______

User Alan Cole
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Final answer:

The vertical asymptote(s) do not exist, and the horizontal asymptote is y = +∞.

Step-by-step explanation:

To find the vertical asymptotes of a function, we need to determine the values of x for which the function becomes undefined. In this case, the function f(x) = x² + 3 - x is a polynomial, and polynomials are defined for all real numbers. Therefore, there are no vertical asymptotes (x = does not exist).

To find the horizontal asymptotes, we need to examine the behavior of the function as x approaches positive and negative infinity.

Since the function is a quadratic with a positive leading coefficient (x² term), the graph of the function opens upward and approaches positive infinity as x goes to positive infinity. Therefore, the horizontal asymptote is y = +∞.

User Ebarooni
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