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D
The time of year,
x
Hours of daylight,
D(x)

E
Hours of daylight,
k
Amount of solar energy gained over the day,
E(k)

G
Amount of solar energy,
r
Hours of video games Rafael can play,
G(r)

Which 2 of the following composed functions make sense in this context?
Choose 2 answers:
A
G(E(k))
B
E(D(x))
C
E(G(r))
D
D(E(k))

\begin{tabular}{lll} $\newline$ $D$ & The time of year, $x$ & Hours of daylight, $D(x)$ \\ $\newline$ $E$ & Hours of daylight, $k$ & Amount of solar energy gained over the day, $E(k)$ \\ $\newline$ $G$ & Amount of solar energy, $r$ & Hours of video games Rafael can play, $G(r)$ $\newline$ \end{tabular} $\newline$ Which $2$ of the following composed functions make sense in this context? $\newline$ Choose $2$ answers: $\newline$ A $G(E(k))$ $\newline$ B $x$ $0$ $\newline$ C $x$ $1$ $\newline$ D $x$ $2$

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Write equations of sine functions using properties

Full solution

Q. \begin{tabular}{lll}

\newline

D

& The time of year,

x

& Hours of daylight,

D(x)

\\

\newline

E

& Hours of daylight,

k

& Amount of solar energy gained over the day,

E(k)

\\

\newline

G

& Amount of solar energy,

r

& Hours of video games Rafael can play,

G(r)

\newline

\end{tabular}

\newline

Which

2

of the following composed functions make sense in this context?

\newline

Choose

2

answers:

\newline

A

G(E(k))

\newline

B

x

0

\newline

C

x

1

\newline

D

x

2

Understand Relationships: We need to understand the relationships between the variables given. The time of year $x$ affects the hours of daylight $D(x)$ . The hours of daylight $k$ affect the amount of solar energy gained over the day $E(k)$ . The amount of solar energy $r$ affects the hours of video games Rafael can play $G(r)$ . We need to find composed functions that make sense with these relationships.
Option A Explanation: Option A, $G(E(k))$ , means that the amount of solar energy ( $k$ ) determines the amount of solar energy gained over the day ( $E(k)$ ), and this amount of energy then determines the hours of video games Rafael can play ( $G(r)$ ). This makes sense because the amount of solar energy can influence how much energy is available for playing video games.
Option B Explanation: Option B, $E(D(x))$ , means that the time of year ( $x$ ) determines the hours of daylight ( $D(x)$ ), and the hours of daylight then determine the amount of solar energy gained over the day ( $E(k)$ ). This makes sense because the hours of daylight are directly related to the amount of solar energy received.
Option C Explanation: Option C, $E(G(r))$ , does not make sense because it implies that the hours of video games Rafael can play $(G(r))$ determine the amount of solar energy gained over the day $(E(k))$ , which is not a logical relationship in this context.
Option D Explanation: Option D, $D(E(k))$ , does not make sense because it implies that the amount of solar energy gained over the day ( $E(k)$ ) determines the hours of daylight ( $D(x)$ ), which is not a logical relationship in this context. The hours of daylight should determine the amount of solar energy, not the other way around.

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