Determine if the relation y=4x−1

Question

Determine if the relation  y=4x−1
y
=
4
x
−
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

GPT-4o mini · Answer

To determine if the relation $ y = 4x - 1 $ is a function, we start by recognizing that this equation represents a linear function in slope-intercept form, where $ m = 4 $ is the slope and $ b = -1 $ is the y-intercept. 1. **Graphing the Relation**: The graph of $ y = 4x - 1 $ will be a straight line that passes through the point (0, -1) (the y-intercept) and will have a slope of 4, meaning it rises 4 units for every 1 unit it moves to the right. 2. **Vertical Line Test**: To apply the vertical line test, you can imagine drawing vertical lines (or actually draw vertical lines) at various values of $ x $ on the graph. If any vertical line intersects the graph at more than one point, then the relation is not a function. In this case, since $ y = 4x - 1 $ is a straight line, any vertical line will intersect the graph at exactly one point. Therefore, it passes the vertical line test. Since the relation meets the criteria for being a function, the answer is **1** (indicating that it is a function).