Question

○ $y = f(x) - 5$
(e) reflect about the $x$-axis.
○ $y = f(x - 5)$
○ $y = f(x) + 5$
○ $y = 5f(x)$
○ $y = -f(x)$
○ $y = \frac{1}{5}f(x)$
(f) reflect about the $y$-axis.
○ $y = f(-x)$
○ $y = f(x) + 5$
○ $y = f(x - 5)$
○ $y = \frac{1}{5}f(x)$
○ $y = 5f(x)$
(g) stretch vertically by a factor of 5.
○ $y = f(x) - 5$
○ $y = \frac{1}{5}f(x)$
○ $y = 5f(x)$
○ $y = f(x) + 5$
○ $y = f(x - 5)$
(h) shrink vertically by a factor of 5.
○ $y = 5f(x)$
○ $y = f(x) + 5$
○ $y = f(x - 5)$
○ $y = \frac{1}{5}f(x)$
○ $y = f(x) - 5$

Explanation:

Step1: Identify x-axis reflection rule

Reflecting $y=f(x)$ over the x-axis negates the output: $y=-f(x)$.

Step2: Identify y-axis reflection rule

Reflecting $y=f(x)$ over the y-axis negates the input: $y=f(-x)$.

Step3: Identify vertical stretch rule

Stretching $y=f(x)$ vertically by factor $a$ gives $y=af(x)$; here $a=5$, so $y=5f(x)$.

Step4: Identify vertical shrink rule

Shrinking $y=f(x)$ vertically by factor $a$ gives $y=\frac{1}{a}f(x)$; here $a=5$, so $y=\frac{1}{5}f(x)$.

Answer:

(e) $y = -f(x)$
(f) $y = f(-x)$
(g) $y = 5f(x)$
(h) $y = \frac{1}{5}f(x)$