Vocabulary
Power Function- A function in the form a=ax^b, where a is a real number and b is a rational number.
Composition- The composition of a function g with a function f is h(x)=g(f(x)).
Composition- The composition of a function g with a function f is h(x)=g(f(x)).
Essential Information
Operations on Functions
Let f and g be any two functions. A new function h can be defined by performing any of the four basic operations on f and g.
Addition h(x)=f(x)+g(x) h(x)=5x+(x+2)=6x+2
Subtraction h(x)=f(x)-g(x) h(x)=5x-(x+2)=4x-2
Multiplication h(x)=(f(x))(g(x)) h(x)=5x(x+2)=5x^2+10x
Division h(x)=f(x)/g(x) h(x)=(5x)/(x+2)
The domain of h consists of the x values that are in the domains of both f and g. Additionally, the domain of the quotient does not include x-values for which g(x)=0.
Power Functions
There are several kinds of functions, including linear, polynomial functions, and quadratic. There is also a function known as the power function in the form y=ax^b, where a is a real number and b is a rational number.
Let f and g be any two functions. A new function h can be defined by performing any of the four basic operations on f and g.
Addition h(x)=f(x)+g(x) h(x)=5x+(x+2)=6x+2
Subtraction h(x)=f(x)-g(x) h(x)=5x-(x+2)=4x-2
Multiplication h(x)=(f(x))(g(x)) h(x)=5x(x+2)=5x^2+10x
Division h(x)=f(x)/g(x) h(x)=(5x)/(x+2)
The domain of h consists of the x values that are in the domains of both f and g. Additionally, the domain of the quotient does not include x-values for which g(x)=0.
Power Functions
There are several kinds of functions, including linear, polynomial functions, and quadratic. There is also a function known as the power function in the form y=ax^b, where a is a real number and b is a rational number.