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Question 4 • Algebra II

Which of the following graphs represents a function?

Answer

Image with description Coordinate plane with x-axis and y-axis labeled from negative 5 to 5. A sideways parabola opens to the right. The vertex is at negative 3 comma 3. From the vertex, the upper branch curves upward and right, passing through approximately 0 comma 4.8 and continuing upward as indicated by an arrow. The lower branch curves downward and right, passing through approximately 0 comma 1.2 and continuing toward 5 comma 0 as indicated by an arrow. The graph is symmetric about the horizontal line y equals 3.

Image with description Coordinate plane with x-axis labeled from negative 5 to 5 and y-axis labeled from negative 3 to 3. A piecewise graph is shown. A decreasing curve extends from the left and joins a straight line at the point 1 comma 0.5. The curve passes through negative 5 comma 1.4 and decreases to 1 comma 0.5. From 1 comma 0.5, a straight line decreases to the right, crossing the x-axis at 2 comma 0 and continuing downward through 5 comma negative 2. Arrows at both ends indicate the graph continues beyond the displayed window.

Image with description A coordinate plane with x-axis from negative 5 to 5, y-axis from negative 5 to 5 , has 7 points. The points are (negative 4 comma 3) comma (negative 2 comma negative 5) comma (negative 1 comma negative 3) comma (1 comma 3) comma (2 comma negative 2) comma (4 comma negative 2) comma (4 comma 2).

Image with description Coordinate plane with x-axis labeled from negative 3 to 3 and y-axis labeled from negative 5 to 5. An ellipse is centered on the y-axis and symmetric about both the x-axis and y-axis. The ellipse intersects the x-axis at negative 2 comma 0 and 2 comma 0, and intersects the y-axis at 0 comma 3.5 and 0 comma negative 3.5. The ellipse is taller than it is wide, extending from approximately negative 2 to 2 horizontally and from approximately negative 3.5 to 3.5 vertically.

Explanation

A graph represents a function if each x-value corresponds to only one y-value, which is the vertical line test. In B, every vertical line intersects the graph at most once, so it represents a function. A and D fail because some vertical lines cross their sideways parabola or ellipse twice. C fails because the two points with x = 4 have different y-values, −2 and 2.

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