N/A — Exam

Question 34 • Algebra II

Which of the following graphs represents a function?

Answer

Image with description On a coordinate plane,with x-axis from negative 5 to 5, y-axis from 3 to negative 3 , a graph shows an image of a curved line connected to a straight line. The curved line is upward facing and goes through the y-axis at (0 comma 0.5). The curved line connects with the straight line at (1 comma 0.5). The straight line has a negative slope and goes through the x-axis at (1.8 comma 0).

Image with description On a coordinate plane, with x-axis from negative 5 to 5, y-axis from 3 to negative 3, a circle intercepts the x-axis at points (negative 2 comma 0) and (2 comma 0) and intercepts the y-axis between points 3 and 4 and also between points negative 3 and negative 4.

Image with description On a coordinate plane comma with x-axis from negative 5 to 5, y-axis from negative 5 to 5 , a parabola opens to right and has a vertex at (negative 3 comma 3).

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).

Explanation

A graph represents a function if every vertical line crosses it at most once, so each x-value has only one y-value. In A, the curved and straight pieces meet at (1, 0.5), and the graph gives one y-value for each x. The circle in B and the right-opening parabola in C fail the vertical-line test, and D has two points with x = 4.

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