Finding a Horizontal Stretch for a Tabular Function

The formula $g(x)=f\left(\frac{1}{2}x\right)$ tells us that the output values for $g$ are the same as the output values for the function $f$ at an input half the size. Notice that we do not have enough information to determine $g(2)$ because $g(2)=f\left(\frac{1}{2}\cdot 2\right)=f(1),$ and we do not have a value for $f(1)$ in our table. Our input values to $g$ will need to be twice as large to get inputs for $f$ that we can evaluate. For example, we can determine $g(4)\text{.}$

We do the same for the other values to produce Table 14.

Figure 25 shows the graphs of both of these sets of points.

Figure 25