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K McMullen 2012
Maths MethodsTypes of Functions 2
K McMullen 2012
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
Types Of Functions
The power form of a quadratic functionf(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
Types Of Functions
The power form of a quartic functionf(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
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
Types Of Functions
The power form of the cubic functiona 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
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
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
Types of Functions
Graphs of functions with fractional powersf(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
Types of Functions
Graphs of functions with fractional powersf(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
Types of Functions
Graphs of functions with fractional powersf(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
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
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
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