Problem
2. Write the function $g(x)$ that results from applying each of the following transformations to the parent function $f(x)=x$ a) Translation 2 units to the right and 5 units up b) Horizontal stretch of factor 2 c) Reflected across the $x$-axis d) Translated 2 units to the left, then reflected across the $y$-axis, then vertically compresses by a factor of $\frac{1}{2}$
Solution
Step 1 ：g(x) = f(x-2) + 5
Step 2 ：g(x) = 2f(x) = 2x
Step 3 ：g(x) = -f(x) = -x
Step 4 ：g(x) = \frac{1}{2}f(-x+2) = \frac{1}{2}(-x+2)
