Determine if the relation y=4x−1

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.

GPT-4o mini · Answer

To determine if the relation $ y = 4x - 1 $ is a function, we can follow these steps: 1. **Understanding the relation**: This is a linear equation in the form of $ y = mx + b $, where $ m = 4 $ (the slope) and $ b = -1 $ (the y-intercept). 2. **Graphing the relation**: This line can be graphed by plotting the y-intercept at $ -1 $ (which is the point $ (0, -1) $) and then using the slope to find another point. From the y-intercept, you can go up 4 units and right 1 unit to find another point at $ (1, 3) $. Connecting these points gives you a straight line. 3. **Applying the vertical line test**: The vertical line test states that if a vertical line crosses the graph of a relation at more than one point, then the relation is not a function. Since a straight line (like the one described by $ y = 4x - 1 $) can be intersected by any vertical line at most once, we conclude that this relation passes the vertical line test. Therefore, $ y = 4x - 1 $ **is a function**. So, the answer is: **1** (indicating that the relation is a function).