![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](https://image.slidesharecdn.com/typesoffunctions2-120213192728-phpapp02/85/Types-of-functions2-3-320.jpg)
![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](https://image.slidesharecdn.com/typesoffunctions2-120213192728-phpapp02/85/Types-of-functions2-4-320.jpg)
Types of functions2
- 1. Maths Methods Types of Functions 2 K McMullen 2012
- 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