Question

does this graph represent a function? why or why not?
a. no, because it fails the vertical line test.
b. no, because it is not a straight line.
c. yes, because it passes the horizontal line test.
d. yes, because it passes the vertical line test.

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if no vertical line intersects it more than once. The given graph, when checked with vertical lines, will have each \( x \)-value corresponding to only one \( y \)-value (passes the vertical line test). Option A is wrong (it does not fail the vertical line test), B is wrong (a function doesn’t have to be a straight line), C is wrong (horizontal line test is for one - to - one functions, not for being a function). So the correct reasoning is that it passes the vertical line test, meaning it is a function.

Answer:

D. Yes, because it passes the vertical line test.