4. Describe how the graph of $y=f(x)$ can be transformed to the graph of
a) $y=f[2(x-1)]+5$
b) $y=f\left(-\frac{1}{2} x+6\right)+1$
Answer
The graph of $y = f\left(-\frac{1}{2} x+6\right)+1$ is produced by taking the graph of $y = f(x)$, reflecting it in the y-axis, stretching it horizontally by a factor of 2, shifting six units to the left, and then shifting one unit upwards.
Step 1 ：The graph of $y = f[2(x-1)]+5$ is produced by taking the graph of $y = f(x)$, compressing it horizontally by a factor of 2, shifting one unit to the right, and then shifting five units upwards.
Step 2 ：The graph of $y = f\left(-\frac{1}{2} x+6\right)+1$ is produced by taking the graph of $y = f(x)$, reflecting it in the y-axis, stretching it horizontally by a factor of 2, shifting six units to the left, and then shifting one unit upwards.
