Question

a definition for a function, f, is shown.

$f(x)=\frac{1}{x - 3}-\frac{5}{(x - 3)(x - 2)}$

which choice describes $x = 3$ for the function?

a a zero of f

b a vertical asymptote of f

c the location of a relative minimum of f

d the location of a removable discontinuity of

Explanation:

Step1: Simplify the function

First, find a common denominator for the two fractions. The common denominator of \(x - 3\) and \((x - 3)(x+2)\) is \((x - 3)(x + 2)\).

$$
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Step2: Analyze the function

We can cancel out the \((x - 3)\) terms (for \(x
eq3\)), and we get \(f(x)=\frac{1}{x + 2}\) for \(x
eq3\). A removable discontinuity occurs when a factor in the numerator and denominator cancels out.

Answer:

D. the location of a removable discontinuity of \(f\)