Graph the function and identify the domain and range. solve it and tell me why

Question

y = –6x2
(1 point)
Responses

A parabola opening down is graphed on a coordinate plane with vertex at (0, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is less than or equal to 0.

domain: (–∞,∞)

range: y ≤ 0
Image with alt text: A parabola opening down is graphed on a coordinate plane with vertex at (0, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is less than or equal to 0. domain: (–∞,∞) range: y ≤ 0

A parabola opening up is graphed on a coordinate plane with vertex at (0, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is greater than or equal to 0.

domain: (–∞,∞)

range: y ≥ 0
Image with alt text: A parabola opening up is graphed on a coordinate plane with vertex at (0, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is greater than or equal to 0. domain: (–∞,∞) range: y  ≥ 0

A parabola opening up is graphed on a coordinate plane with vertex at (2, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is greater than or equal to 0.

domain: (–∞,∞)

range: y ≥ 0
Image with alt text: A parabola opening up is graphed on a coordinate plane with vertex at (2, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is greater than or equal to 0. domain: (–∞,∞) range: y ≥ 0

A parabola opening up is graphed on a coordinate plane with vertex at (negative 2, 0). Domain is labeled left parenthesis negative infinity, infinity right parenthesis. Range is: y is greater than or equal to 0.

domain: (–∞,∞)

range: y ≥ 0

GPT 3.5 · Answer

The correct response is:

A parabola opening down is graphed on a coordinate plane with vertex at (0, 0). The domain is all real numbers since the function is defined for all x values. The range is y ≤ 0.

Therefore,
Domain: (-∞, ∞)
Range: y ≤ 0

The graph of the function y = -6x^2 is a parabola that opens downwards. The vertex of the parabola is at (0, 0). The domain of the function is all real numbers since the function is defined for all x values. The range is all real numbers less than or equal to 0 because the parabola is entirely below the x-axis.