Select the domain and range of the function below. You must pick one of each for credit.

Question

the graph shows a curved line that passes through (-1.2,0) (0,-2) (1.2,0)

(2 points)
Responses

{x | −2≤x <∞}
{x | −2≤x <∞}

{y | −2≤y <∞}
{y | −2≤y <∞}

{x | −∞<x <∞}
{x | −∞<x <∞}

{y | −∞<y<∞}
{y | −∞<y<∞}

{y | −∞<y ≤−2}

Answer 1

To determine the domain and range of the function based on the given information about the graph, we analyze the coordinates provided and the nature of the curve.

Domain:

• The function appears to have x-values that range from -1.2 to 1.2, and it is possible to have values outside this interval as it does not specify any vertical asymptotes or discontinuities. However, since there is no indication that it continues indefinitely, the more reasonable interpretation is that x-values are between -1.2 and 1.2.

Thus, the proper selection for the domain based on the x-values is:

• {x | -∞ < x < ∞} (the function can take any real number as input around the observed points).

Range:

• The y-values at the specified points are:
  • At (-1.2, 0) the y-value is 0.
  • At (0, -2) the y-value is -2.
  • At (1.2, 0) the y-value is again 0.

From the information given, it appears that the graph is a curved line reaching as low as -2 and returning to 0 at both ends. Given that the lowest point is -2 and the graph does not drop below it, the range must reflect this.

The most fitting choice for the range is:

• {y | -2 ≤ y < ∞} (the function reaches a maximum of -2 but could rise indefinitely).

Therefore, the selections for domain and range would be:

• Domain: {x | -∞ < x < ∞}
• Range: {y | -2 ≤ y < ∞}