Practice Test

Question 1 • Mathematics 8

Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x ?

Answer

Image with description A Cartesian coordinate plane with horizontal x- and vertical y-axes labeled from negative 4 to 4. A circle is centered at the origin (0 comma 0) with a radius of 4 units. A vertical line with arrowheads at both ends passes through x equals 1, intersecting the circle at two points marked with solid dots, approximately at (1 comma 3.9) and (1 comma negative 3.9).

Image with description A Cartesian coordinate plane with horizontal x- and vertical y-axes labeled from negative 4 to 4. A circle is centered at the origin (0 comma 0) with a radius of 4 units. A horizontal line with arrowheads at both ends passes through y equals 2, intersecting the circle at two points marked with solid dots, approximately at (negative 3.5 comma 2) and (3.5 comma 2).

Image with description A Cartesian coordinate plane with horizontal x- and vertical y-axes labeled from negative 4 to 4. A circle is centered at the origin (0 comma 0) with a radius of 4 units, passing through (4 comma 0), (0 comma 4), (negative 4 comma 0), and (0 comma negative 4). A horizontal line with arrowheads at both ends passes through y equals 4 and is tangent to the circle at the point (0 comma 4), which is marked with a solid dot.

Image with description A Cartesian coordinate plane with horizontal x- and vertical y-axes labeled from negative 4 to 4. A circle is centered at the origin (0,0) with a radius of 4 units, passing through (4 comma 0), (0 comma 4), (negative 4 comma 0), and (0 comma negative 4). A vertical line with arrowheads at both ends passes through x equals negative 4 and is tangent to the circle at the point (negative 4 comma 0), which is marked with a solid dot.

Explanation

The vertical line test checks whether any vertical line intersects the graph more than once. In choice A, the vertical line at x = 1 crosses the circle at two points, so the same x-value has two different y-values. Therefore, the circle is not a function of x. The horizontal lines in choices B and C do not demonstrate this test, and the vertical line in D touches the circle only once.

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