Functions Unit Test

Question

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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)

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can follow these steps:

1. Graph the equation: The equation \( y = 4x - 1 \) is a linear equation, representing a straight line with a slope of 4 and a y-intercept of -1. You can graph it easily by plotting a few points. For example:

   • When \( x = 0 \), \( y = 4(0) - 1 = -1 \) → Point (0, -1)
   • When \( x = 1 \), \( y = 4(1) - 1 = 3 \) → Point (1, 3)
   • When \( x = -1 \), \( y = 4(-1) - 1 = -5 \) → Point (-1, -5)

   These points can then be connected to form a straight line.

2. Apply the vertical line test: The vertical line test states that if any vertical line intersects the graph of the relation at more than one point, the relation is not a function. Since the graph of \( y = 4x - 1 \) is a straight line, any vertical line will intersect it at exactly one point.

Since the relation passes the vertical line test, we can conclude that \( y = 4x - 1 \) is indeed a function.

Final answer: Enter 1 if the relation is a function. Therefore, the answer is 1.