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Let $f(x) = 5\sin(x)+5$ and $g(x) = -5\sin(x)+5$ .

(a) Which of the following is the graph of $f(x)$ ?

(b) Which of the following is the graph of $g(x)$ ?



A	B	C	D

Answer the following about the function $f(x)$ :

.
(d) The amplitude of $f(x)$ is

.
(e) The midline of $f(x)$ is $y =$

(f) Choose the statement that best describes the starting behavior of $f(x)$ . That is, what happens as $f(x)$ crosses the vertical axis?

A. $f(x)$ crosses the vertical axis at the midline and increases as the input values get bigger.
B. $f(x)$ crosses the vertical axis at the midline and decreases as the input values get bigger.
C. $f(x)$ crosses the vertical axis at its maximum value and decreases as the input values get bigger.
D. $f(x)$ crosses the vertical axis at its minimum value and increases as the input values get bigger.

Answer the following about the function $g(x)$ :

(g) The period of $g(x)$ is

.
(h) The amplitude of $g(x)$ is

.
(i) The midline of $g(x)$ is $y =$

(j) Choose the statement that best describes the starting behavior of $g(x)$ . That is, what happens as $g(x)$ crosses the vertical axis?

A. $g(x)$ crosses the vertical axis at the midline and increases as the input values get bigger.
B. $g(x)$ crosses the vertical axis at the midline and decreases as the input values get bigger.
C. $g(x)$ crosses the vertical axis at its maximum value and decreases as the input values get bigger.
D. $g(x)$ crosses the vertical axis at its minimum value and increases as the input values get bigger.

(k) Choose the statements below that can describe the differences between the two functions $f(x)$ and $g(x)$ .

A. $f(x)$ and $g(x)$ are both vertical stretches and shifts of $\sin(x)$ , but $g(x)$ is also a reflection of $\sin(x)$ across the horizontal axis.
B. $f(x)$ and $g(x)$ are both vertical stretches and shifts of $\sin(x)$ , but $g(x)$ is also a reflection of $\sin(x)$ across the vertical axis.
C. $g(x)$ is the function $f(x)$ reflected across the horizontal axis.
D. $g(x)$ is the function $f(x)$ reflected across the vertical axis.
E. $f(x)$ and $g(x)$ are the same function.

Hint

a)-b) Keep in mind how sine usually behaves at the vertical axis.

k) What does a horizontal reflection of $\sin(x)$ look like? What does a vertical reflection of $\sin(x)$ look like?