Input-Output Relationships — Test

Question 23 • Mathematics 8

Which graph is a function of x ?

Answer

Image with description Coordinate plane with x- and y-axes labeled. Both axes range from negative 4 to 4 in increments of 2. A vertical line with arrowheads at both ends passes through x equals negative 3.

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. A graph resembling the letter V has its vertex at (1 comma 0) and passes through the points (0 comma 3) and (2 comma 3).

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. Two curves on the plane resemble the sideways letter Vees, with one opening to the right and the other to the left. The vertex of the first V is at (negative 1 comma 0) and passes through the points (negative 4 comma 4) and (negative 4 comma negative 4). The vertex of the second V is at (1 comma 0) and passes through the points (4 comma 4) and (4 comma negative 4).

Image with description Coordinate plane with x- and y-axes labeled. Both axes range from negative 4 to 4 in increments of 2. A sideways curve has its leftmost point at (negative 3 comma 1). Two branches extend to the right with arrowheads. The upper branch passes through approximately (0 comma 3) and continues upward to the right. The lower branch passes through approximately (0 comma negative 1) and continues downward to the right.

Explanation

A graph is a function of x if every vertical line intersects it at most once. In choice B, the upright V has exactly one y-value for each x-value, so it passes the vertical line test. Choice A is itself a vertical line, while the sideways graphs in C and D have some x-values paired with more than one y-value.

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