Question

Determine if the relation y = 4x - 1 is a function by first graphing the relation, then applying the vertical line test. Is the relation a function? * 1 point Yes No

Answer 1

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

1. **Graph the Relation**: The equation \( y = 4x - 1 \) is a linear equation, which represents a straight line with a slope of 4 and a y-intercept of -1.

2. **Apply the Vertical Line Test**: The vertical line test is a method used to determine whether a relation is a function. If a vertical line intersects the graph at more than one point, then the relation is not a function.

Since \( y = 4x - 1 \) is a linear equation and represents a straight line, any vertical line drawn will intersect the line at exactly one point.

Based on these observations:

- **Does the graph pass the vertical line test?** Yes, any vertical line intersects the graph at most one time.

Therefore, the relation \( y = 4x - 1 \) is indeed a function.

**Final answer: Yes**.