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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.

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Review

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  1. Review Domain and Range Composition of Functions Variation

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

  3. Range • All possible values of y which make a function true • Written in set notation

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

  5. 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.

  6. 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))

  7. 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

  8. Inverse Variation • y is inversely proportional to x • y varies inversely as x • y=k/x

  9. 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

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