Question

1. when using a table to graph a function, what is the vertical line test checking for?

a. whether each x - value has exactly one y - value
b. whether each y - value has exactly one x - value
c. whether the function is linear
d. whether the function passes through the origin

Explanation:

The vertical line test is a method to determine if a graph represents a function. A function is defined as a relation where each input (x - value) has exactly one output (y - value). The vertical line test checks if any vertical line drawn on the graph intersects the graph more than once. If it does not, then each x - value has exactly one y - value. Option B is incorrect because a function can have multiple x - values for a single y - value (e.g., \(y = x^{2}\), where \(x = 1\) and \(x=- 1\) both give \(y = 1\)). Option C is incorrect because the vertical line test does not check if a function is linear (a non - linear function like \(y=x^{2}\) can still be a function and pass the vertical line test). Option D is incorrect because the vertical line test has nothing to do with whether the function passes through the origin.

Answer:

A. Whether each x - value has exactly one y - value