Determine if the relation Y equals 4X minus one is a function by first graphing the relation, then applying the vertical line test. Enter one if the relation is a function. Answer two if the relation is not a function.

Answer 1

To determine if the relation \( Y = 4X - 1 \) is a function, we can examine its graph and use the vertical line test.

1. Graphing the relation: The equation \( Y = 4X - 1 \) is in slope-intercept form \( Y = mx + b \) where \( m = 4 \) and \( b = -1 \). This means the graph is a straight line with a slope of 4, and it intersects the Y-axis at -1.

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. For a linear equation like \( Y = 4X - 1 \), it is a straight line.

Since a vertical line will intersect the straight line at only one point regardless of where you draw it, we conclude that this relation passes the vertical line test.

Therefore, \( Y = 4X - 1 \) is a function.

In conclusion, the answer is 1 (the relation is a function).