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.(1 po int)

GPT-4o mini · Answer

To determine if the relation $ y = 4x - 1 $ is a function, we can start by understanding what it represents. 1. **Graph the relation:** The equation $ y = 4x - 1 $ represents a straight line in the Cartesian coordinate system. It has a slope of 4 and a y-intercept of -1. - When $ x = 0 $, $ y = -1 $ (the line crosses the y-axis at (0, -1)). - When $ x = 1 $, $ y = 4(1) - 1 = 3 $ (the line passes through (1, 3)). - When $ x = -1 $, $ y = 4(-1) - 1 = -5 $ (the line also passes through (-1, -5)). The line will continue infinitely in both directions. If you graph this equation, you will see a straight line. 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 it is not a function. Since the graph of $ y = 4x - 1 $ is a straight line, any vertical line drawn will intersect the graph at exactly one point. Therefore, the relation passes the vertical line test. Based on the above reasoning: - Since the relation $ y = 4x - 1 $ is represented by a straight line and passes the vertical line test, it is indeed a function. So the answer is **1** (the relation is a function).