IXL - Domain and range of polynomials (Precalculus practice)

This is the graph of a polynomial function. There is no absolute minimum or maximum.

Find the domain and range.

(-∞, ∞)

(-∞, -3]

(-∞, ∞)

[-3, ∞)

Domain:

Range:

ref_doc_title.

Learn with an example

question

This is the graph of a polynomial function. The absolute minimum is shown on the graph.

Find the domain and range.

(-∞, ∞)

[-4, ∞)

(-∞, ∞)

(-∞, 4]

Domain:

Range:

key idea

The domain of a function is the set of all

-values

that can be inputs of the function.

The range of a function is the set of all

-values

that are outputs of the function.

Interval notation can be used to describe sets of real numbers.

The symbols [ and ] are used to indicate that an endpoint is included.
The symbols ( and ) are used to indicate that an endpoint is not included.
The symbols for positive infinity, ∞, and negative infinity,
–
∞
, are used to show that a set continues forever in one direction or the other.

For example, the interval

(

–

]

is the same as

–

≤

and the interval

[

∞

)

is the same as

≥

solution

Find the domain.

Every

-value

is a valid input for a polynomial function. The arrows on the polynomial function mean that it continues on forever for all

-values.

So, the domain is the set of all real numbers, which is written

(

–

∞

)

Find the range.

Not every

-value

is an output of this polynomial function.

The function has an absolute minimum value of

–

This means that smaller

-values,

such as

–

100

are not in the range.

Larger

-values,

such as

–

or 50, are in the range. The arrows on the polynomial function both point upward. So, the function continues on forever, hitting all of the

-values

larger than the absolute minimum.

The range is the set of real numbers that are greater than or equal to

–

which is written

[

–

∞

)

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Teacher tools

Work it out

Not feeling ready yet? These can help:

F.10Match polynomials and graphs

G.3Interval notation

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