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)

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can analyze it based on its definition and then apply the vertical line test conceptually.

1. **Graphing the relation**:
The equation \( y = 4x - 1 \) is in the slope-intercept form \( y = mx + b \), where \( m = 4 \) and \( b = -1 \). This means that the graph is a straight line with a slope of 4 and a y-intercept at (0, -1).

2. **Applying the vertical line test**:
The vertical line test states that if a vertical line intersects the graph of a relation at more than one point, then the relation is not a function. Since the graph of \( y = 4x - 1 \) is a straight line, any vertical line will intersect it at exactly one point.

Since every vertical line intersects the graph of \( y = 4x - 1 \) at exactly one point, we conclude that the relation is indeed a function.

Therefore, you should enter **1**. The relation is a function.