Question
determine if the relationship 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 or enter 2 if the relation is non function
Answers
GPT-4o mini
To determine if the relation \( y = 4x - 1 \) is a function, we can analyze it through its graph and the vertical line test.
1. **Graphing the Relation**:
The equation \( y = 4x - 1 \) is a linear equation. When you graph it, you will see a straight line. The line crosses the y-axis at \(-1\) (the y-intercept) and has a slope of \(4\), which means for every one unit you move to the right along the x-axis, you move up four units on the y-axis.
2. **Applying the 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 the relation is not a function. Since the graph of \( y = 4x - 1 \) is a straight line, any vertical line drawn will intersect it exactly once.
Since the graph passes the vertical line test, we can conclude that the relation \( y = 4x - 1 \) is indeed a function.
Therefore, you should enter **1** to indicate that the relation is a function.
1. **Graphing the Relation**:
The equation \( y = 4x - 1 \) is a linear equation. When you graph it, you will see a straight line. The line crosses the y-axis at \(-1\) (the y-intercept) and has a slope of \(4\), which means for every one unit you move to the right along the x-axis, you move up four units on the y-axis.
2. **Applying the 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 the relation is not a function. Since the graph of \( y = 4x - 1 \) is a straight line, any vertical line drawn will intersect it exactly once.
Since the graph passes the vertical line test, we can conclude that the relation \( y = 4x - 1 \) is indeed a function.
Therefore, you should enter **1** to indicate that the relation is a function.