Which of the following gives the correct range for the graph?

A coordinate plane with a segment going from the point negative 4 comma negative 2 to 0 comma negative 1 and another segment going from the point 0 comma negative 1 to 3 comma 5.
−2 ≤ x ≤ 5
−2 ≤ y ≤ 5
−4 ≤ x ≤ 3
−4 ≤ y ≤ 3

1 answer

To determine the correct range for the graph depicted by the points given, we need to evaluate the y-values represented by those points.

  1. The points provided are:
    • From \((-4, -2)\) to \((0, -1)\)
    • From \((0, -1)\) to \((3, 5)\)

Now we will extract the y-values from these points:

  • The y-values from the first segment, from point \((-4, -2)\) to \((0, -1)\), are:

    • \(-2\) (from the point \((-4, -2)\))
    • \(-1\) (from the point \((0, -1)\))
  • The y-values from the second segment, from point \((0, -1)\) to \((3, 5)\), are:

    • \(-1\) (from the point \((0, -1)\))
    • \(5\) (from the point \((3, 5)\))

Now we can identify the minimum and maximum y-values across both segments:

  • The minimum y-value is \(-2\) (the lowest point from the first segment).
  • The maximum y-value is \(5\) (the highest point from the second segment).

Thus, the range of the y-values is: \[ -2 \leq y \leq 5 \]

Next, we also need to consider the x-values which progress as follows:

  • The x-values from the first segment range from \(-4\) to \(0\).
  • The x-values from the second segment range from \(0\) to \(3\).

The overall x-range therefore is from: \(-4\) (the x-value from the first segment) to \(3\) (the x-value from the second segment).

Thus, the range of x-values is: \[ -4 \leq x \leq 3 \]

Given the options you provided, we have determined:

  • For y-values: \(−2 ≤ y ≤ 5\)
  • For x-values: \(−4 ≤ x ≤ 3\)

The correct answers based on the y-values is: \(-2 ≤ y ≤ 5\)

Therefore, the final answer is: −2 ≤ y ≤ 5.