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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) $y = 1 - x$ $\newline$ (B) $y = x$ $\newline$ (C) $x - y = 1$ $\newline$ (D) $x = 1$ $\newline$ (E) $y = -x - 1$

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Find derivatives of sine and cosine functions

Full solution

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 = 1 - x

\newline

(B)

y = x

\newline

(C)

x - y = 1

\newline

(D)

x = 1

\newline

(E)

y = -x - 1

Analyze Equation (A): Analyze equation (A) $y = 1 - x$ . $\newline$ - This equation can be rewritten for any $x$ to find a corresponding $y$ . $\newline$ - It's a function because for each $x$ , there is exactly one $y$ .
Analyze Equation (B): Analyze equation (B) $y = x$ . $\newline$ - Direct relationship where each $x$ corresponds to one $y$ . $\newline$ - Clearly a function.
Analyze Equation (C): Analyze equation (C) $x - y = 1$ . $\newline$ - Rearrange to $y = x - 1$ . $\newline$ - Each $x$ value gives one $y$ value, so it's a function.
Analyze Equation (D): Analyze equation (D) $x = 1$ . $\newline$ - This equation does not define $y$ as a function of $x$ ; it's just a vertical line. $\newline$ - Not a function because it doesn't pass the vertical line test.
Analyze Equation (E): Analyze equation (E) $y = -x - 1$ . $\newline$ - Similar to (A) and (B), each $x$ corresponds to one $y$ . $\newline$ - It's a function.

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