What are the domain and range of the polynomial function shown?

Question

The coordinate grid has x and y axes labeled from negative 5 to 5. The graph of a cubic function is shown.

(1 point)
Responses

Domain: (−∞, ∞); Range: (−∞, ∞)
Domain: open paren negative infinity comma infinity close paren ; Range: open paren negative infinity comma infinity close paren

Domain: (−∞, ∞); Range: [−1, ∞)
Domain: open paren negative infinity comma infinity close paren ; Range: left bracket negative 1 comma infinity right parenthesis

Domain: (−∞, −1]; Range: (−∞, ∞)
Domain: left parenthesis negative infinity comma negative 1 right bracket ; Range: open paren negative infinity comma infinity close paren

Domain: (−∞, −1]; Range: [−1, ∞)

Answer 1

For a polynomial function, specifically a cubic function, the domain is always all real numbers, which can be represented as \( (-\infty, \infty) \).

The range of a cubic function can be all real numbers (i.e., \( (-\infty, \infty) \)) or may have a minimum or maximum depending on the specific graph of the function. Given that you describe the graph as a cubic function, if it extends infinitely in both y-directions, the range would also be all real numbers.

Based on the options provided, the correct choice would be:

Domain: \( (-\infty, \infty) \); Range: \( (-\infty, \infty) \)

So the response is: Domain: (−∞, ∞); Range: (−∞, ∞)