Question

On a coordinate plane, a v-shaped line crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and the x-axis at (2, 0).
What is the domain of the function on the graph?

all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0

Answer 1

To determine the domain of the function represented by the V-shaped line that crosses the x-axis at the points \((-2, 0)\) and \((2, 0)\) as well as the y-axis at \((0, -2)\), let's analyze the points:

1. The points where the graph intersects the x-axis at \((-2, 0)\) and \((2, 0)\) suggest that the graph extends from \(x = -2\) to \(x = 2\).
2. The graph is V-shaped, indicating that it continues between those x-values but does not extend beyond \(x = -2\) and \(x = 2\).

Since there are no restrictions mentioned about values outside the intersections, the graph can be represented as including all x-values between and including \(-2\) and \(2\).

Thus, the domain of the function on the graph is:

\[
[-2, 2]
\]

Since the provided options do not explicitly list this, the closest description that might apply under the constraint of your options would be "all real numbers greater than or equal to -2" when considering non-negative values visually; however, it does not fully capture the actual domain.

In summary, the graph’s domain is:
\[
-2 \leq x \leq 2
\]

But based on your options, none of them correctly represent the complete domain of the function according to the provided points on the coordinate plane. If you must select an answer from these options alone, be aware that a more precise choice is not available.