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 point)

Explanation:

Step1: Analyze the relation type

The relation \( y = 4x - 1 \) is a linear equation in the form \( y=mx + b \) (where \( m = 4 \), \( b=-1 \)). Linear equations of this form (non - vertical lines) represent functions. But we can also use the vertical line test.

Step2: Apply vertical line test

For a vertical line \( x = a \) (where \( a \) is any real number), substitute \( x=a \) into \( y = 4x-1 \). We get \( y=4a - 1 \), which is a single value for \( y \) for each \( x=a \). So, any vertical line will intersect the graph of \( y = 4x - 1 \) at most once. So the relation passes the vertical line test.

Answer:

1