Which of the following equations represent functions where x is the input and y is the output? Select all that apply. Multi-select Choices: (A)y = 0 (B)y - 2x = 6 (C)2x - y = 6 (D)y = x^3 (E)y = x^2

Question

Which of the following equations represent functions where x is the input and y is the output? Select all that apply.   Multi-select Choices: (A)y = 0 (B)y - 2x = 6 (C)2x - y = 6 (D)y = x^3 (E)y = x^2

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Identify Function Criteria:  Step 1: Identify if each equation represents a function where x is the input and y is the output. A function must assign exactly one output for each input. Check Equation (A):  Step 2: Check equation (A) y = 0. This equation means y is always 0, regardless of x. This is a valid function because every x has exactly one y (0). Check Equation (B):  Step 3: Check equation (B) y - 2x = 6. Rearrange to y = 2x + 6. This is a linear equation where for each x, there is exactly one y. This is a function. Check Equation (C):  Step 4: Check equation (C) 2x - y = 6. Rearrange to y = 2x - 6. Similar to (B), this is a linear equation and a function. Check Equation (D):  Step 5: Check equation (D) y = x^3. This is a cubic equation. For each x, there is exactly one y. This is a function. Check Equation (E):  Step 6: Check equation (E) y = x^2. This is a quadratic equation. For each x, there is exactly one y. This is a function.

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) $y = 0$ $\newline$ (B) $y - 2x = 6$ $\newline$ (C) $2x - y = 6$ $\newline$ (D) $y = x^3$ $\newline$ (E) $y = x^2$

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