How do we describe the
Domain and Range of a
function?
Do Now: What are all values that
we can plug into the equation
x3
y 2
x 4
What is the Domain of a
function?
• The domain of a function is the set of
every value that can be plugged into the
function.
• In the Do Now, the Domain is the set of all
real numbers except ±2
• This can be written as R/{±2}
What is the Range of a
function?
• The range is the set of numbers that
can come out of the function.
• Often it is more difficult to find the range
than it is to find the domain
Type
Example
Domain
Range
Linear
y=2x-1
All real
All real
Quadratic
y=x2-4
y=-2x2+4x+5
All real
y≥-4
y≤5
Cubic
y=x3+6
All real
All real
Absolute
Value
y= 2x-3
All real
y≥0
All real
except
x=-5
x≤10
y≥0
Rational
Functions with
radicals

3x 1
y
x5
y  10  x
Examples
• Determine the largest possible domain
for each function
3x 1
f (x)  2
x  3x  4
7x
g(x) 
5  2x

h(x)  2x  4

Try on your own
• Determine the largest possible domain
and range for each function
2
f (x)  x  10
3
g(x)  x  8x  15
2

h(x)  3  4 x
Summary/HW
• How does the type of function impact its
domain and range?
• HW: pg 152-3, 1-21 odd