Determine if the relation y = 4x - 1 is a function by first graphing the

Question

Determine if the relation y = 4x - 1 is a function by first graphing the
relation, then applying the vertical line test. Enter 1 if the relation is a function. Enter 2 if the relation is not a function. (1 point)

GPT-4o mini · Answer

To determine if the relation $ y = 4x - 1 $ is a function, we can follow two steps: graphing the relation and applying the vertical line test. 1. **Graphing the Relation**: The equation $ y = 4x - 1 $ describes a linear function, where the slope is 4 and the y-intercept is -1. When graphed, it will produce a straight line. 2. **Applying the Vertical Line Test**: To check if this relation defines $ y $ uniquely for each $ x $, we imagine drawing vertical lines on the graph. The vertical line test states that if any vertical line intersects the graph at more than one point, the relation is not a function. Since $ y = 4x - 1 $ is a straight line, any vertical line will intersect it at exactly one point. Since the line passes the vertical line test, the relation $ y = 4x - 1 $ is indeed a function. Thus, the answer is **1** (indicating that it is a function).