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Describe the shifts/reflections that can be applied to $f(x)$ to obtain a graph of the following:

a) $y=-f(x)$

A. Reflect the graph of $f(x)$ over the $y$ -axis.
B. Shift the graph of $f(x)$ up by 1.

C. Shift the graph of $f(x)$ left by 1.

D. Reflect the graph of $f(x)$ over the $x$ -axis.

b) $y = f(x-9)$

A. Shift the graph of $f(x)$ up by 9.

B. Shift the graph of $f(x)$ down by 9.

C. Shift the graph of $f(x)$ right by 9.

D. Shift the graph of $f(x)$ left by 9.

c) $y = f(x)+10$

A. Shift the graph of $f(x)$ up by 10.

B. Shift the graph of $f(x)$ down by 10.

C. Shift the graph of $f(x)$ right by 10.

D. Shift the graph of $f(x)$ left by 10.

d) $-f(-x)$

A. Reflect the graph of $f(x)$ over the $y$ -axis.
B. Shift the graph of $f(x)$ up by 1.

C. Reflect the graph of $f(x)$ over the $x$ -axis.
D. Reflect the graph of $f(x)$ over the $y$ -axis and over the $x$ -axis.

e) $y=f(-x)$

A. Shift the graph of $f(x)$ left by 1.

B. Reflect the graph of $f(x)$ over the $y$ -axis.
C. Reflect the graph of $f(x)$ over the $x$ -axis.
D. Shift the graph of $f(x)$ up by 1.

f) $y = f(x)-10$

A. Shift the graph of $f(x)$ left by 10.

B. Shift the graph of $f(x)$ right by 10.

C. Shift the graph of $f(x)$ down by 10.

D. Shift the graph of $f(x)$ up by 10.

Hint: