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 When do we say that a function is linear, quadratic,
polynomial, rational, or radical?
 How can you find the domain and range of a function?

Domain of a function
the set of all values of the independent variable that have corresponding values
of the dependent variable
1
Example:
Consider the function .
The domain of is the set containing all the first coordinates.

Range of a function
the set of all values of that can be obtained from the possible values of
2
Example:
Consider the function .
The range of is the set containing all the second coordinates.

Linear function
a function that has a degree of 1 and whose graph is a straight line; the domain
and range of a linear function are both the set of real numbers
3
Example:
The functions and are linear functions.

Quadratic function
a function that has a degree of 2 and whose graph is a parabola; the domain of a
quadratic function is the set of real numbers
4
Example:
The functions and are quadratic functions.

Polynomial function
a function involving nonnegative integer powers of the independent variable; the
domain of a polynomial function is the set of real numbers; the range of a
polynomial function whose degree is odd is the set of real numbers
5
Example:
The functions and are polynomial functions.
Constant, linear, and quadratic functions are also polynomial
functions.

Rational function
a function that can be expressed as a ratio of two polynomials; the domain of a
rational function is the set of real numbers except the zeros of its denominator
6
Example:
The functions and are rational functions.
The domain of is the set of real numbers except .
The domain of is the set of real numbers except .

Radical function
a function that contains radical expressions; the domain of a radical function is
the set of real numbers except those that make the radicand of radicals with
even index negative
7
Example:
The functions and are radical functions.
What do you think are the domain of and the domain of ?

Example 1: Find the domain and range of the function .

Answer:
The function is a linear function. The domain and range of
a linear function are both the set of the real numbers.
Therefore, the domain of the function is and its range is
also .
Example 1: Find the domain and range of the function .

Example 2: Find the domain and range of .

Solution:
For a square root function to be defined, the radicand
must be nonnegative (i.e. greater than or equal to zero).
Example 2: Find the domain and range of .
Therefore, the domain of is and
its range is since the principal
square root a number is always
nonnegative.

Individual Practice:
1. What is the domain and range of .
2. Find the domain and range of using its graph.

Group Practice: To be done by 2-5 groups
A ball is thrown upward with an initial velocity of 32 ft/s from
a height of 10 ft. The height at any given time is given by
What is the domain and range of this function?

Domain of a function
the set of all values of the independent variable that have corresponding values
of the dependent variable
1
Range of a function
the set of all values of that can be obtained from the possible values of
2
Linear function
a function that has a degree of 1 and whose graph is a straight line; the domain
and range of a linear function are both the set of real numbers
3

Quadratic function
a function that has a degree of 2 and whose graph is a parabola; the domain of a
quadratic function is the set of real numbers
4
Polynomial function
a function involving nonnegative integer powers of the independent variable; the
domain of a polynomial function is the set of real numbers; the range of a
polynomial function whose degree is odd is the set of real numbers
5
Rational function
a function that can be expressed as a ratio of two polynomials; the domain of a
rational function is the set of real numbers except the zeros of its denominator
6

Radical function
a function that contains radical expressions; the domain of a radical function is
the set of real numbers except those that make the radicand of radicals with
even index negative
7

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FUNCTIONS AND RELATION DOMAIN AND RANGE OF FUNCTIONS.pptx

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