Question

What is the range of the function graphed below?​

Answer 1

Answer:

Range: $y\in[-4,0)\cup[2,+\infty)$

Step-by-step explanation:

Range of a Function

Given a real function f(x), the Range of f is the set of all the values the function can take when x varies within the domain of f.

If we have the graph of the function, a practical rule can be used to find the Range. Imagine a horizontal rule moving from minus infinity to plus infinity. If that rule touches the graph of the function, the vertical height or y-value belongs to the range.

Consider the function provided in the image. If our horizontal rule comes from minus infinity, it won't touch the graph until it reaches the value y=-4. Note the endpoint has a filled dot, meaning the point belongs to the function. The range starts from -4.

Going up in values of y, we touch the function until y=0. But that endpoint is marked with an empty dot, so that point does not belong to the function.

The first interval of the range is [-4,0)

Moving up the rule, we touch the function again when y=2 (included) and we note the function continues to go up to plus infinity (signaled with the arrow). Thus, the second interval is [2,+∞).

The range of f is the union of both intervals:

Range: $y\in[-4,0)\cup[2,+\infty)$