Question

which of the following graphs represents a function? select all that apply.
a)

b)

c)

d)

Explanation:

Step1: Recall Vertical Line Test

A graph represents a function if no vertical line intersects the graph more than once.

Step2: Analyze Graph a

For graph a, if we draw a vertical line, it will intersect the graph at more than one point (the curve crosses a vertical line twice in some regions), so it is not a function.

Step3: Analyze Graph b

For graph b, any vertical line drawn will intersect the graph at most once. So it passes the vertical line test and represents a function.

Step4: Analyze Graph c

For graph c (a parabola opening upwards), any vertical line drawn will intersect the graph at most once. So it passes the vertical line test and represents a function.

Step5: Analyze Graph d

For graph d (a circle), a vertical line through the circle will intersect it at two points, so it fails the vertical line test and is not a function.

Answer:

b) The graph in option b, c) The graph in option c