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 funon. Enter 2 if the relation is not a function

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can analyze its characteristics.

1. Graphing the Relation: The equation \( y = 4x - 1 \) represents a straight line with a slope of 4 and a y-intercept of -1. When you graph it, you will see a straight line that extends infinitely in both the positive and negative directions.

2. Vertical Line Test: The vertical line test states that if a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Since \( y = 4x - 1 \) is a linear equation, any vertical line will intersect this line at exactly one point. Thus, it passes the vertical line test.

Since the relation passes the vertical line test, we conclude that it is indeed a function.

Thus, the answer is 1 (indicating that the relation is a function).