Question

structure select the domain and range of the function in interval notation. determine whether the function is one-to-one, onto, both, or neither. then state whether it is discrete, continuous, or neither discrete nor continuous.
domain = select choice
range = select choice
the function is select choice and select choice

Explanation:

Step1: Identify domain (x-values)

The graph covers all real x-values except $x=0$, so domain is $(-\infty,0) \cup (0,\infty)$.

Step2: Identify range (y-values)

The graph covers all real y-values, so range is $(-\infty,\infty)$.

Step3: Check one-to-one

Passes horizontal line test: no horizontal line intersects graph more than once, so it is one-to-one.

Step4: Check onto

Every real y-value is achieved by the function, so it is onto.

Step5: Check continuity

The graph has no breaks except at $x=0$ (not in domain), so it is continuous.

Answer:

Domain: $(-\infty,0) \cup (0,\infty)$
Range: $(-\infty,\infty)$
The function is one-to-one and onto, and it is continuous.