Worked out by Jakubíková K. 1
Math Worksheet 3 – DOMAIN and RANGE
Given a function y = f(x), the Domain of the function is the set of inputs and the Range is
the set of resulting outputs.
Domains can be found algebraically; ranges are often found algebraically and
graphically. Domains and Ranges are sets. Therefore, you must use proper set notation.
Algebraic method:
When finding the domain of a function, ask yourself what values can't be used. Your
domain is everything else. There are simple basic rules to consider:
- The domain of all polynomial functions is the Real numbers R.
1156)( 23 xxxxf
)
Since f(x) is a polynomial, the domain of f(x) is R. It can also be written
,
- Square root functions can not contain a negative underneath the radical. Set the
expression under the radical greater than or equal to zero and solve for the variable.
This will be your domain.
ttg 32)(
Since g(t) is a square root, set the expression under the radical to greater than or equal
to zero: 2 - 3t 0 2 3t 2/3 t. Therefore, the domain of g(t) =
,
3
2
- Rational functions can not have zeros in the denominator. Determine which values of
the input cause the denominator to equal zero, and set your domain to be everything
else.
4
1
)( 2
p
p
ph
- Since h(p) is a rational function, the bottom can not equal zero. Set p2 - 4 = 0 and
solve: p2 - 4 = 0 (p + 2)(p - 2) = 0 p = -2 or p = 2. These two p values need to
be avoided, so the domain of h(p) = R –{ -2 or 2 } or
),2()2,2()2,(
The – minus is read as "except".
Graphical method:
Function y = √(x + 4) has the following graph
The domain of the function is x ≥ −4, since x
cannot take values less than −4.
D(f) = <-4, ∞)
The range of a function is the possible y values
of a function that result when we substitute
all the possible x-values into the function.
Make sure you look for minimum and maximum
values of y.
We say that the range for this function is y ≥ 0
R(f) = <0,∞) (in Slovakia H(f) = <0,∞) – obor hodnôt)
