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Which of the following equations represent functions where $x$ is the input and $y$ is the output? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $y = 0.25x$ $\newline$ (B) $y = \frac{2}{5}$ $\newline$ (C) $x - y = 25$ $\newline$ (D) $y = 25 - 5x$ $\newline$ (E) $y = 5^x$

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Find derivatives of sine and cosine functions

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Q. Which of the following equations represent functions where

x

is the input and

y

is the output? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

y = 0.25x

\newline

(B)

y = \frac{2}{5}

\newline

(C)

x - y = 25

\newline

(D)

y = 25 - 5x

\newline

(E)

y = 5^x

Analyze equation (A): Step $1$ : Analyze equation (A) $y = 0.25x$ . $\newline$ - This equation shows $y$ as a function of $x$ because for each $x$ , there is exactly one corresponding $y$ value.
Analyze equation (B): Step $2$ : Analyze equation (B) $y = \frac{2}{5}$ . $\newline$ - This equation shows $y$ as a constant value, not depending on $x$ ; hence, it's still a function because each $x$ corresponds to one $y$ (always $\frac{2}{5}$ ).
Analyze equation (C): Step $3$ : Analyze equation (C) $x - y = 25$ . $\newline$ - Rearrange to $y = x - 25$ . This shows $y$ as a function of $x$ , as each $x$ value gives one $y$ value.
Analyze equation (D): Step $4$ : Analyze equation (D) $y = 25 - 5x$ . $\newline$ - This equation also shows $y$ as a function of $x$ , with each $x$ value uniquely determining a $y$ value.
Analyze equation (E): Step $5$ : Analyze equation (E) $y = 5^x$ . $\newline$ - This equation represents $y$ as a function of $x$ , where $y$ changes based on the value of $x$ , and each $x$ has one $y$ .

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