Question

does this graph represent a function? why or why not? a. no, because it fails the vertical line test. b. yes, because it is a curved line. c. no, because it is not a straight line. 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 is a parabola opening upwards (vertex at the origin). When we apply the vertical line test, any vertical line will intersect this parabola at most once. So it passes the vertical line test, meaning it is a function. Let's analyze the options:

• Option A: Incorrect, as the graph does not fail the vertical line test.
• Option B: Incorrect, a curved line isn't the reason for being a function (e.g., a circle is curved but not a function).
• Option C: Incorrect, the graph is a function, and being non - straight doesn't determine that.
• Option D (assuming the last option is "Yes, because it passes the vertical line test"): Correct, as the graph passes the vertical line test.

Answer:

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