Question

question 1 of 10
does this graph represent a function?
graph of a parabola with vertex at (-2, 0), opening upwards, x-axis labeled with -4, -3, -2, -1, 1; y-axis labeled with -1, 1, 2, 3
a. yes, because it touches the y-axis exactly one time
b. no, because some of the y-values are paired with two x-values
c. no, because there are no closed circles to show where the graph ends
d. yes, because each x-value has exactly one corresponding y-value

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if every vertical line intersects it at most once (i.e., each \( x \)-value has exactly one \( y \)-value).

• Option A: Touching the \( y \)-axis once is not the definition of a function. Eliminate A.
• Option B: A function allows multiple \( x \)-values to map to the same \( y \)-value (e.g., a parabola), so this reasoning is incorrect. Eliminate B.
• Option C: Closed circles for endpoints are irrelevant to the function definition. Eliminate C.
• Option D: The graph (a parabola opening upwards) passes the vertical line test: each \( x \)-value has exactly one \( y \)-value. This matches the function definition.

Answer:

D. Yes, because each \( x \)-value has exactly one corresponding \( y \)-value