Question

decide whether the equation $y = x - 4$ is a function.

choose the correct answer below.

a. the equation is not a function.

b. the equation is a function.

Explanation:

Step1: Apply Vertical Line Test

A relation is a function if every vertical line intersects its graph at most once. The equation $y = x - 4$ is a linear equation, whose graph is a straight line with slope $1$ and y-intercept $-4$.

Step2: Verify Input-Output Mapping

For any input $x$, there is exactly one calculated value of $y$: $y = x - 4$. No single $x$-value produces more than one $y$-value.

Answer:

B. The equation is a function.