Question

structure select the domain and range of the function in interval notation. determine whether the function is one-to-one, both, or neither. then state whether it is discrete, continuous, or neither discrete nor continuous.
domain = $(-\infty, \infty)$
range = $(-\infty, \infty)$
the function is not one-to-one and continuous

Explanation:

Step1: Identify domain (x-values)

The graph extends infinitely left/right, so all real numbers are allowed. Domain: $(-\infty, \infty)$

Step2: Identify range (y-values)

The graph extends infinitely up/down, so all real y-values are covered. Range: $(-\infty, \infty)$

Step3: Test one-to-one (horizontal line test)

Any horizontal line intersects the graph exactly once, so it is one-to-one.

Step4: Check continuity

The graph has no breaks, gaps, or jumps, so it is continuous.

Answer:

Domain = $(-\infty, \infty)$
Range = $(-\infty, \infty)$
The function is one-to-one and continuous