Question

Use the image to answer the question.

Four points are plotted on a coordinate plane, forming a parabolic curve.
The x-axis ranges from negative 6 to 4 in increments of 1. The y-axis ranges from negative 18 to 5 in increments of 1. The vertex of the parabola has coordinates left parenthesis negative 1 comma negative 16 right parenthesis. The following points are marked on the parabola: left parenthesis negative 5 comma 0 right parenthesis, left parenthesis negative 2 comma negative 15 right parenthesis, left parenthesis 0 comma negative 15 right parenthesis, and left parenthesis 3 comma 0 right parenthesis.


The quadratic function f(x)=x^(2)+2x−15
is shown in the graph. Determine the domain and range of this function.

(1 point)
Responses

domain R
; range R

domain the real numbers ; range the real numbers

domain R
; range y≥16

domain the real numbers ; range y is greater than or equal to 16

domain R
; range y≥−16

domain the real numbers ; range y is greater than or equal to negative 16

domain R
; range y≤−16

domain negative infinity less-than-or-equal-to x less-than-or-equal-to infinity ; range y is less than or equal to negative 16

Answer 1

Domain: all real numbers (R). Range: y ≥ −16.

Justification: The parabola opens upward (leading coefficient 1 > 0) with vertex at (−1, −16), so the minimum value is −16 and y takes all values ≥ −16.