Which graph represents a function?

On a coordinate plane, a line with 2 angles crosses the x-axis at (negative .5, 0), the y-axis at (0, 1), turns at (1, 3), crosses the x-axis at (1, 0), turns at (1, negative 2), and crosses the x-axis at (2, 0).

On a coordinate plane, a curved line crosses the y-axis at (0, 1.5), the x-axis at (negative 2, 0), and the y-axis at (0, negative 1.5).

On a coordinate plane, a line enters the plane at point (negative 5, 4), makes a 90-degree turn at (negative 1, 0), and leaves the plane at point (negative 5, negative 4).

On a coordinate plane, a line with an s curve enters the plane at point (negative 3.75, 5), crosses the x-axis at (negative .75, 0), the y-axis at (0, 0), leaves x-axis at (.75, 0), and exits the plane at point (3.75, negative 5).

1 answer

To determine which graph represents a function, we can use the vertical line test. A graph represents a function if no vertical line can intersect the graph at more than one point.

  1. Graph 1: The description mentions multiple x-values where the graph crosses the x-axis at points (negative 0.5, 0), (1, 0), and (2, 0) which indicates multiple outputs (y-values) for a single input (x-value) at some points. Hence, this does not represent a function.

  2. Graph 2: Given that the description refers to a curved line that crosses the y-axis at (0, 1.5) and the x-axis at (negative 2, 0) and (0, negative 1.5), it does not indicate multiple outputs for the same input. This could represent a function, but further information about the structure of the graph would be needed to be sure.

  3. Graph 3: A line that makes a 90-degree turn at (negative 1, 0) and exits the plane at (negative 5, negative 4) remains single-valued for each x value. Thus, this may represent a function.

  4. Graph 4: The description indicates this line has an "s" curve and crosses the x-axis multiple times for different y-values, indicating that it likely has multiple outputs for some inputs. This does not represent a function.

Based solely on the vertical line test and given the descriptions, Graph 3 is likely the clearest representation of a function, as it forms one continuous line without intersecting itself at any vertical line.