2. Types Of Functions
Graphs of f(x)=xn where n is an even positive
integer
The graphs of even functions are symmetrical
about the y-axis
The maximal domain of the power function is R
and the range is [0, ∞)
A function is even if f(-x)=f(x) for all values of x in
the domain of f
Many-to-one function; every y value has a
corresponding –x and x value
K McMullen 2012
3. Types Of Functions
The power form of a quadratic function
f(x)=a(x-b)2+c
a is the dilation factor from the x-axis
The turning point is at (b,c)
The equation of the axis of symmetry is the line x=b
The domain is R
The range is [c, ∞) if a>0 or (-∞,c] if a<0
b is the translation along the x-axis
c is the translation along the y-axis
K McMullen 2012
4. Types Of Functions
The power form of a quartic function
f(x)=a(x-b)4+c
a is the dilation factor from the x-axis
The turning point is at (b,c)
The equation of the axis of symmetry is the line x=b
The domain is R
The range is [c, ∞) if a>0 or (-∞,c] if a<0
b is the translation along the x-axis
c is the translation along the y-axis
K McMullen 2012
5. Types Of Functions
Graphs of f(x)=xn where n is an odd positive
integer
As n increases, the branches of the curve move
closer to the y-axis
The maximal domain of the function is R and the
range is R
A function is odd if f(-x)=-f(x) for all values of x in
the domain of x
K McMullen 2012
6. Types Of Functions
The power form of the cubic function
a is the dilation factor from the x-axis
(b,c) is the stationary point of inflection
The domain is R
The range is R
b is the translation along the x-axis
c is the translation along the y-axis
K McMullen 2012
7. Types of Functions
Graphs of f(x)=1/xn where n is a positive odd
integer
Maximal domain is R{0}
Range is R{0}
One-to-one and odd functions
Asymptotes at x=0 and y=0
K McMullen 2012
8. Types of Functions
Graphs of f(x)=1/xn where n is a positive even
integer
Maximal domain is R{0}
Range is R+
Many-to-one and even functions
Asymptotes at x=0 and y=0
K McMullen 2012
9. Types of Functions
Graphs of functions with fractional powers
f(x)=xp/q
p and q are both positive odd integers with highest
common factor of 1
Domain is R
Range is R
K McMullen 2012
10. Types of Functions
Graphs of functions with fractional powers
f(x)=xp/q
p is a positive even integer and q is a positive odd
integer with highest common factor of 1
Domain is R
Range is R+∪{0}
K McMullen 2012
11. Types of Functions
Graphs of functions with fractional powers
f(x)=xp/q
p is a positive odd integer and q is a positive even
integer with highest common factor of 1
Domain is R+∪{0}
Range is R+∪{0}
K McMullen 2012
12. Types of Functions
Graphs of functions with negative fractional
powers
f(x)=x-p/q
p and q are both positive odd integers with highest
common factor of 1
Domain is R+∪{0}
Range is R+∪{0}
Asymptotes at x=0 and y=0
K McMullen 2012
13. Types of Functions
Graphs of functions with negative fractional
powers
f(x)=x-p/q
p is a positive even integer and q is a positive odd
integer with highest common factor of 1
Domain is R+{0}
Range is R+
Asymptotes at x=0 and y=0
K McMullen 2012
14. Types of Functions
Graphs of functions with negative fractional
powers
f(x)=x-p/q
p is a positive odd integer and q is a positive even
integer with highest common factor of 1
Domain is R+
Range is R+
Asymptotes at x=0 and y=0
K McMullen 2012
