Question

in each box, determine if graphs a and b represent y as a function of x. in each white rectangle, type \graph a\, \graph b\, \both\ or
either\.

Explanation:

Step1: Use the vertical line test

For a graph to represent \(y\) as a function of \(x\), any vertical line drawn on the graph should intersect the graph at most once.

Step2: Analyze the first box (purple)

• Graph A: A vertical line will intersect it more than once. So it is not a function.
• Graph B: A vertical line will intersect it at most once. So it is a function.

Step3: Analyze the second box (green)

• Graph A: A vertical line will intersect it at most once. So it is a function.
• Graph B: A vertical line (e.g., near the vertex of the "U - shape" opening to the right) will intersect it more than once. So it is not a function.

Step4: Analyze the third box (yellow)

• Graph A: A vertical line will intersect it at most once. So it is a function.
• Graph B: A vertical line will intersect it at most once. So it is a function.

Step5: Analyze the fourth box (blue)

• Graph A: A vertical line will intersect it at most once. So it is a function.
• Graph B: A vertical line will intersect it at most once. So it is a function.

Answer:

First box: Graph B; Second box: Graph A; Third box: Both; Fourth box: Both