Question

Determine whether each function is continuous at the given x-value. Justify your answer using the continuity test.

f(x)={3x+5 if x4x+2 if x>4;x=4f(x)=\left\{\begin{array}{l} 3 x+5 \text { if } x \leq-4 \\ -x+2 \text { if } x>-4 \end{array} ; x=-4\right.

Solution

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Given function:

f(x)={3x+5,x4x+2,x>4; x=4\boxed{f(x)=\begin{cases}3x+5&, x\le -4\\-x+2&, x>-4 \end{cases}; \ x=-4}

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