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 $\frac{1}{2}$

Answer

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Answer

g(x) = \frac{1}{2}f(-x+2) = \frac{1}{2}(-x+2)

Steps

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)

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