The Function h(x) is defined as shown. What is the range of h(x)?

Step-by-step explanation:

Piecewise Function

The given function has a point where its behavior changes. At the left side of x=3 the function is

While at the right side the function is

We need to find the range of h, i.e. the values h takes when x moves along its domain. Let's analyze what values takes h when x decreases without limit.

When x=3

When x increses without limit

As shown, the values of h run from to 5, i.e.

Or, equivalently

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