Question
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
A y-intercept and decreasing interval
An increasing interval and x-intercept
An x-intercept and decreasing interval
An increasing interval and y-intercept
Answers
GPT-4o mini
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**.
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**.