Question

true or false: the equation $y = -3$ is a function. enter 1 for true or 2 for false. (1 point)

Explanation:

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value). For the equation \(y=-3\), no matter what value \(x\) takes, \(y\) is always \(-3\). So for every \(x\) (input), there is exactly one \(y\) (output, which is \(-3\)).

Step2: Apply vertical line test

The vertical line test states that if any vertical line drawn on the graph of a relation intersects the graph at more than one point, the relation is not a function. The graph of \(y = - 3\) is a horizontal line parallel to the \(x\) - axis. Any vertical line \(x=a\) (where \(a\) is any real number) will intersect the line \(y=-3\) at exactly one point \((a,-3)\). So by the vertical line test, \(y = - 3\) is a function.

Answer:

1