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Which of the following equations represent functions? Assume $x$ is the input and $y$ is the output. $\newline$ Multi-select Choices: $\newline$ (A) $x = -1$ $\newline$ (B) $y = x$ $\newline$ (C) $y = 1$ $\newline$ (D) $x + y = 1$ $\newline$ (E) $x = 0$

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Full solution

Q. Which of the following equations represent functions? Assume

x

is the input and

y

is the output.

\newline

Multi-select Choices:

\newline

(A)

x = -1

\newline

(B)

y = x

\newline

(C)

y = 1

\newline

(D)

x + y = 1

\newline

(E)

x = 0

Identify Uniqueness: Identify if each equation uniquely determines $y$ as a function of $x$ .
Check Expression: Check if $y$ can be expressed uniquely for each $x$ .
Evaluate Determination: Evaluate if the equation defines $y$ uniquely in terms of $x$ .
Determine Rearrangement: Determine if the equation can be rearranged to express $y$ as a function of $x$ .
Check Involvement: Check if the equation involves $y$ and if it can be expressed as a function of $x$ .

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