Review Domain and Range Composition of Functions Variation

Domain �All possible values of x which make the function true �Written in set notation �All real number

Range �All possible values of y which make a function true �Written in set notation

Set builder notation �Used for domain and range �x can have constraints �x is an element of, , real numbers

Interval notation �Used for domain and range �x is an element greater then 4 but less than or equal to 19. �( or ) represent that the number is NOT included, whereas [ or ] include the number.

Composition of Functions �Functions can be added, subtracted or composed. �Adding �Combine like terms from both functions �f(x)+g(x) �Subtracting �A function is subtracted from the other (make sure to distribute your negatives!) �f(x)-g(x) �A composition of functions is substituting one function into another �f(g(x)) �g(f(2))

Direct Variation �y varies directly as x �y is proportional to x �y=kx �K is the constant of proportionality �Joint Variation �y varies jointly with x and z �y=kxz

Inverse Variation �y is inversely proportional to x �y varies inversely as x �y=k/x

Practice Problems �What is the domain? �What is the range? � Find g(f(x)) �R is proportional to I, the cube of b and inversely proportional to P and t