Lesson #3: Introduction to the Basic Parent Functions
Lesson #3:
Introduction to the
Basic Functions—
Parent Functions
MoreonFunctions: Onto Functions
A function from set A to set B is onto if the range
of the function is equal to set B. (all of the range
values are used.)
Example:
Since all of the elements
in Set B are used, this
function is onto.
The range of this function
is equal to set B.
Algebra II/Trigonometry: Unit 1
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Lesson #3: Introduction to the Basic Parent Functions
Onto Functions
Example1:Determineifthegivenfunctionis
ontoornot.Explain.
Since all of the
elements in Set B are
NOT used, this function
is NOT onto.
The range of this
function is NOT equal to
set B.
Onto Functions
Example2:Determineifthegivenfunctionis
ontoornot.Explain.
Since all of the elements
in Set B are NOT used,
this function is NOT onto.
The range of this function
is NOT equal to set B, all
real numbers.
*Note: The possible range (Set B) of a
function located on the -coordinate
plane is always all real numbers or
∞, ∞ .
Algebra II/Trigonometry: Unit 1
2
Lesson #3: Introduction to the Basic Parent Functions
Onto Functions
Example3:Determineifthegivenfunctionis
ontoornot.Explain.
Since all of the elements
in Set B are used, this
function is onto.
The range of this function
is all real numbers.
Onto Functions
Example4:Determineifthegivenfunctionis
ontoornot.Explain.
Since all of the elements
in Set B are NOT used,
this function is NOT onto.
The range of this function
is NOT equal to set B.
Algebra II/Trigonometry: Unit 1
3
Lesson #3: Introduction to the Basic Parent Functions
Onto Functions
Example5:Determineifthegivenfunctionis
ontoornot.Explain.
Since all of the elements
in Set B are NOT used,
this function is NOT onto.
The range of this function
is NOT equal to set B, all
real numbers.
Types of Functions
1. Constant Functions
If the slope of a linear function is 0, or
then the linear function becomes
or
This relation is called a constant function.
Basic
Parent
Function
0,
.
Domain:
∞, ∞
Range:
,
or
*Note: The equation
is NOT a constant
function because the graph is a vertical line
which does not pass the vertical line test.
Algebra II/Trigonometry: Unit 1
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Lesson #3: Introduction to the Basic Parent Functions
Types of Functions
2. Linear Functions
Any equation in the form
is a function whose graph is a straight line.
Remember:
is the slope and
is the -intercept.
Basic
Parent
Function
Domain:
∞, ∞
Range:
∞, ∞
Types of Functions
3. Quadratic Functions
Any equation in the form
, where
0 is a quadratic function whose graph is a
parabola that has a vertical line of symmetry.
Basic
Parent
Function
Domain:
∞, ∞
Range:
,∞
*Note: Quadratics in the form of
where
0 are not functions.
Algebra II/Trigonometry: Unit 1
,
5
Lesson #3: Introduction to the Basic Parent Functions
Types of Functions
4. Absolute Value Functions
These functions are in the form
.
Every value of x corresponds to one and only one value of y.
Basic
Parent
Function
y
Domain:
∞, ∞
Range:
,∞
*Note: Absolute value equations in
the form
are not
functions because they do not pass
the vertical line test.
Types of Functions
5. Cubic Functions
Any equation in the form
where
0 is a cubic function.
Basic
Parent
Function
,
Domain:
∞, ∞
Range:
∞, ∞
Algebra II/Trigonometry: Unit 1
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Lesson #3: Introduction to the Basic Parent Functions
Types of Functions
6. Square Root Functions
Any equation in the form
0 is a square root function.
, where
Domain:
Basic
Parent
Function
,∞
Range:
,∞
Types of Functions
7. Cube Root Functions
Any equation in the form
0 is a cube root function.
, where
Basic
Parent
Function
Domain:
∞, ∞
Algebra II/Trigonometry: Unit 1
Range:
∞, ∞
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Lesson #3: Introduction to the Basic Parent Functions
Types of Functions
8. Exponential Functions
Any equation in the form
is an exponential function.
, where
BasicParent
Function
0
Domain:
∞, ∞
Range:
0,1
where
,∞
,
Types of Functions
9. Reciprocal Functions
Any equation in the form
, where
0
is a reciprocal function whose graph is a hyperbola.
BasicParent
Function
where
Algebra II/Trigonometry: Unit 1
Domain:
∞,
∪
,∞
Range:
∞,
∪
,∞
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