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# Types of functions2

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### Types of functions2

1. 1. Maths MethodsTypes of Functions 2 K McMullen 2012
2. 2. Types Of FunctionsGraphs of f(x)=xn where n is an even positiveinteger 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. 3. Types Of FunctionsThe 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. 4. Types Of FunctionsThe 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. 5. Types Of FunctionsGraphs of f(x)=xn where n is an odd positiveinteger 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. 6. Types Of FunctionsThe 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. 7. Types of FunctionsGraphs of f(x)=1/xn where n is a positive oddinteger 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. 8. Types of FunctionsGraphs of f(x)=1/xn where n is a positive eveninteger 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. 9. Types of FunctionsGraphs 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. 10. Types of FunctionsGraphs 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. 11. Types of FunctionsGraphs 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. 12. Types of FunctionsGraphs of functions with negative fractionalpowers 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. 13. Types of FunctionsGraphs of functions with negative fractionalpowers 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. 14. Types of FunctionsGraphs of functions with negative fractionalpowers 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