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.

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can follow these steps:

1. **Graphing the relation**: The equation \( y = 4x - 1 \) represents a linear equation, specifically a straight line with a slope of 4 and a y-intercept of -1.

2. **Applying the vertical line test**: The vertical line test states that if a vertical line intersects the graph of the relation more than once at any point, then the relation is not a function.

For the equation \( y = 4x - 1 \), it is a straight line. Therefore, if you imagine drawing vertical lines at any point on the x-axis, they will intersect the line only once at that point.

Since no vertical line intersects the graph more than once, we can conclude that this relation is indeed a function.

Thus, the answer is:

**1** (the relation is a function).