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Sketch the graph of the function. Label on the graph the coordinates of any relative extrema,...

Question:

Sketch the graph of the function. Label on the graph the coordinates of any relative extrema, points of inflection, asymptotes, intercepts.

{eq}f(x) = \frac{x^2 - 6x + 12}{x - 4} {/eq}

Inflection Points and Asymptotes:

It is important to know which are the inflection points where a change in the concavity of the function occurs.

In the same sense, if the function does not have inflection points, this does not mean that its concavity does not change.

That is, the concavity change can occur at points where the function is not defined as in a vertical asymptote.

Answer and Explanation:

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The function is:

{eq}f(x) = \frac{x^2 - 6x + 12}{x - 4} \\ {/eq}

Relative Extreme

We classify the critical points of a function in relative...

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