Question

the table below gives values for a continuous function f at selected values of x. let g(x)=af(x + c), such that the graph of g results in the following transformation on the graph of f: a horizontal translation to the right 5 units followed by a vertical stretch by a factor of 1/2. what is the value of g(4)?
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$$\begin{tabular}{|c|c|c|c|c|c|c|c|} \\hline x& - 4& - 1&2&4&5&8&9 \\\\ \\hline f(x)& - 10& - 4& - 54& - 16&4& - 22& - 6 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Determine horizontal translation

For a horizontal translation to the right 5 units, we set $x + c=4 - 5=-1$.

Step2: Determine vertical stretch

The vertical - stretch factor $a=\frac{1}{2}$. And $f(-1)=-4$.

Step3: Calculate $g(4)$

$g(4)=\frac{1}{2}f(-1)=\frac{1}{2}\times(-4)=-2$.

Answer:

$-2$