Question

determine if the relation y = 4x - 1 is a function by first graphing the relation

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can analyze its mathematical form and understand it graphically.

1. **Define the Relation**: The equation \( y = 4x - 1 \) is a linear equation, which represents a straight line when graphed.

2. **Graph the Relation**:
- To graph the equation, start by identifying two points:
- When \( x = 0 \):
\[
y = 4(0) - 1 = -1 \quad \text{(Point: (0, -1))}
\]
- When \( x = 1 \):
\[
y = 4(1) - 1 = 3 \quad \text{(Point: (1, 3))}
\]
- Plot the points (0, -1) and (1, 3) on a coordinate plane and draw a straight line through them.

3. **Check Function Criteria**: To confirm if a relation is a function, we can use the **Vertical Line Test**: if any vertical line intersects the graph 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 drawn anywhere on the graph will intersect it at exactly one point.

### Conclusion
Since the line fails to intersect any vertical line more than once, \( y = 4x - 1 \) is indeed a function.