Recognizing Various Representations of Linear Functions

What representations describe a linear function?

To solve this problem, we need to determine which representations describe a linear function by analyzing each given choice:

• Choice 1: $y = 1 - 2x$
  - This is in the form $y = mx + b$, where $m = -2$ and $b = 1$, making it a linear function.
• Choice 2: $y = -2x^2 + x$
  - The term $x^2$ indicates a quadratic polynomial, which is not linear due to the power of 2 on $x$.
• Choice 3: $y = x$
  - In the form $y = mx + b$, it is $y = 1x + 0$, with $m = 1$ and $b = 0$, thus a linear function.
• Choice 4: Asserts that both Choice 1 and Choice 3 are correct, which aligns with our analysis.

Based on this examination, choices forming linear functions are ones where the equation stays in the standard linear form $y = mx + b$ with no additional exponents or variable products. Thus, the correct answer is:

Answers A + C are correct