Question

What is the range of the function graphed below?

Answer 1

Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

Symbols

We need to pay attention to what symbols to use.

Reading the diagram

Solid circle

• The function touches the point.

Empty circle

• The function gets close, but does not touch the point.

Arrow

• The function keeps going to infinity.

Writing range in set notation

Square brackets: [ and ]

• These show that the function touches the point.

Curved brackets: ( and )

• These show that the function gets close but does not touch the point.
• Infinity always uses a curved bracket.

Union of sets: ∪

• This symbol shows that sets of values are talking about the same thing. It's almost like the word 'and'.

Finding the range of the graphed function

Lower blue line

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     $-4$

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     $0$

So, the first part of our range is:

• [–4, 0)

Upper blue line

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    $2$

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    $\infty$

So, the second part of our range is:

• [2, ∞)

Putting it together

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

Learn more about domain and range here:

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