Question

Explain why the function is discontinuous at the given number a. (Select all that apply.) $\begin{aligned} f(x) = \begin{cases} \frac{2x^2 - 7x - 4}{x - 4} & \text{if } x \neq 4\\ 8 & \text{if } x = 4 \end{cases} \end{aligned}$ a = 4 ? $f(4)$ and $\lim_{x \to 4} f(x)$ are finite, but are not equal. ? $f(4)$ is undefined. ? $\lim_{x \to 4^-} f(x)$ and $\lim_{x \to 4^+} f(x)$ are finite, but are not equal. ? $\lim_{x \to 4} f(x)$ does not exist. ? none of the above Sketch the graph of the function.

          Explain why the function is discontinuous at the given number a. (Select all that apply.)
$\begin{aligned} f(x) = \begin{cases} \frac{2x^2 - 7x - 4}{x - 4} & \text{if } x \neq 4\\ 8 & \text{if } x = 4 \end{cases} \end{aligned}$ a = 4
? \(f(4)\) and $\lim_{x \to 4} f(x)$ are finite, but are not equal.
? \(f(4)\) is undefined.
? $\lim_{x \to 4^-} f(x)$ and $\lim_{x \to 4^+} f(x)$ are finite, but are not equal.
? $\lim_{x \to 4} f(x)$ does not exist.
? none of the above
Sketch the graph of the function.

Explain why the function is discontinuous at the given number a. (Select all that apply.)
f(x) = (2x^2 - 7x - 4)/(x - 4) if x ≠ 4
8 if x = 4 a = 4
? f(4) and limx → 4 f(x) are finite, but are not equal.
? f(4) is undefined.
? limx → 4^- f(x) and limx → 4^+ f(x) are finite, but are not equal.
? limx → 4 f(x) does not exist.
? none of the above
Sketch the graph of the function.

Added by William B.

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