Which statement describes the following graph?

image.png
the graph crosses the y-axis at (0,2), increasing from x = -2 to x = 1 and remaining constant from x = 0 to x = 7.
the graph crosses the y-axis at (-0.75,0), increasing from x = -2 to x = 1 and remaining constant x = 0 to x = 7.
The graph crosses the y-axis at (0,2), increasing from x = -2 to x = 1 and remaining constant from x = 0 to x = 7.
The graph crosses the y-axis at (-0.75,0), increasing from x = -2 to x = 1 and remaining constant from x = 1 to x=7.

1 answer

To describe the graph accurately, we need to examine key features such as the y-intercept, behavior over specific intervals, and whether it remains constant.

  1. Y-intercept: Identifies where the graph crosses the y-axis. If it crosses at (0, 2), then the graph would start at the point where x = 0 and y = 2. If it crosses at (-0.75, 0), then the graph would start at x = -0.75 and y = 0.

  2. Increasing Interval: Describes where the graph is rising. The statement indicates it's increasing from x = -2 to x = 1.

  3. Constant Interval: Identifies where the graph doesn't change value. The descriptions suggest that the graph remains constant from either (0 to 7) or (1 to 7).

Given these elements, the statements can be evaluated.

  • Statement Examination:
    • The first two statements mention the graph crossing the y-axis at (0, 2) or (-0.75, 0).
    • The first also states it remains constant from x = 0 to x = 7.
    • The second includes a different constant behavior from 0 to 7, implying contradictions with the y-intercept.

To determine the best option, we would need to identify:

  • Which y-intercept is correct.
  • Whether the intervals are increasing or constant.

Without visual access, I will suggest focusing on the correct y-intercept and constant behavior that matches the given options.

If the graph indeed crosses the y-axis at (0, 2), with correctly identified intervals, the option that aligns with crossing the y-axis there, showing it increased till x=1, and constant till x=7 would be accurate.

So, if it does cross at (0, 2), the best description is: "The graph crosses the y-axis at (0,2), increasing from x = -2 to x = 1 and remaining constant from x = 0 to x = 7."

If it crosses at (-0.75, 0), you would choose the statement that mentions that with an accurate description of increasing and constant segments. Choose the statement that fits the observable behavior based on the true graph presented.