What does (−2, 0) represent on the graph shown?

A y-intercept and decreasing interval

An increasing interval and x-intercept

An x-intercept and decreasing interval

An increasing interval and y-intercept

1 answer

To determine what (−2, 0) represents on a graph, we first recognize that a point is typically represented in the format (x, y). Here, x = -2 and y = 0.

  1. x-intercept: A point where the graph crosses the x-axis occurs when y = 0. Since the y-coordinate is 0 at (−2, 0), this point is an x-intercept.

  2. y-intercept: A point where the graph crosses the y-axis occurs when x = 0. Since the x-coordinate is not 0 at (−2, 0), this point is not a y-intercept.

  3. Increasing/Decreasing Intervals: The classification of intervals as increasing or decreasing depends on the direction of the graph around that point and cannot be determined solely from the coordinates of a single point.

Given that (−2, 0) is an x-intercept and there's no information about increasing or decreasing behavior without additional context about the rest of the graph, the correct representation based on the provided choices would be:

An x-intercept and decreasing interval

This option captures that (−2, 0) is an x-intercept, but the decreasing interval part may need further context. If asked specifically about what (−2, 0) represents, the critical part is that it is an x-intercept.

So the best answer based on your listed options is:

An x-intercept and decreasing interval.