Question

The graph of a piecewise function is shown.
What is the domain of the function?

(−∞, −2) ∪ [2, ∞)
(−∞, −2] ∪ (2, ∞)
(−∞, ∞)
[−∞, ∞]

Answer 1

We must think about the domain of each component before combining them according to the constraints specified in order to identify the domain of a piecewise function. You have two components here:

1. The segment between -2 and negative infinity (exclusive).
2. The portion that runs from 2 to a positive infinity.

Let's evaluate each component:

1. The first part is specified for all values less than -2, hence all real numbers up to but excluding -2 are included in its definition. So, (-, -2) is the domain for this component.

2. Because the second component has a definition for all values greater than 2, all real numbers in the range of 2 to positive infinity are included. So, (2, ) is the domain for this item.

Now, based on the above conditions, we must unite these domains. When combining sets, the union symbol () is utilized. In this situation, it is necessary to integrate the two domains while avoiding any overlaps.

(-, -2) (2, ) is the combined domain.

Answer 2

I had a feeling it was b thank you so much