Questions: Identify the domain, range, and codomain of the graph. Then use the codomain and range to determine whether the function is onto.

Solution Steps

The domain of a function is the set of all possible input values (x-values) for which the function is defined. From the graph, the function appears to extend infinitely in both the positive and negative directions along the x-axis.

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

The range of a function is the set of all possible output values (y-values) that the function can produce. From the graph, the function reaches a maximum value and a minimum value, and it appears to cover all y-values between these two points.

Range: \( [-2, 2] \)

The codomain of a function is the set of all possible output values as defined by the function, which is typically the set of real numbers unless otherwise specified.

Codomain: \( \mathbb{R} \) (the set of all real numbers)

A function is onto (surjective) if every element in the codomain is mapped to by at least one element in the domain. Since the range of the function is \( [-2, 2] \) and the codomain is \( \mathbb{R} \), not every element in the codomain is covered by the range.

The function is not onto.

Final Answer