Question

does the outline represent a function?
a. no, the outline is not a function because a horizontal line cannot be drawn which intersects the outline at more than one point.

b. yes, the outline is a function because a horizontal line can be drawn which intersects the outline at more than one point

c. yes, the outline is a function because a vertical line cannot be drawn which intersects the outline at more than one point

d. no, the outline is not a function because a vertical line can be drawn which intersects the outline at more than one

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 at more than one point. The given graph is a circle. For a circle, we can draw a vertical line (e.g., \( x = 0 \)) that intersects the circle at two points (top and bottom of the circle). So, the outline (circle) does not represent a function because a vertical line can intersect it at more than one point.

Now, let's analyze the options:

• Option A: Talks about horizontal line test, which is for one - to - one functions, not for determining if a graph is a function. Eliminate A.
• Option B: Incorrect, as horizontal line test is not for function definition, and the graph is not a function. Eliminate B.
• Option C: Incorrect, because the graph is not a function (fails vertical line test). Eliminate C.
• Option D: Correct, as it correctly states that the outline is not a function because a vertical line can intersect it at more than one point.

Answer:

D. No, the outline is not a function because a vertical line can be drawn which intersects the outline at more than one point