Ch 6 - Graphing Day 5 - Domain & Range. Domain the set of all inputs that will have an output most types of graphs have the domain of all real numbers.

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Presentation transcript:

Ch 6 - Graphing Day 5 - Domain & Range

Domain the set of all inputs that will have an output most types of graphs have the domain of all real numbers UNLESS: Rational Function Radical Function

Range the set of all output that are possible from a given domain MANY graphs will not have a range of all real numbers! Maximums/Minimums Restricted domains

Linear Functions Are they any restrictions on what you can put into a linear equation? Does the line go on forever without any holes, gaps, asymptotes? Are there any maximums or minimums?

Quadratic Functions Are there any restrictions to the inputs of a quadratic equation? Do quadratics (parabolas) have maximums and minimums? Always or sometimes?

Cubic Functions Are there restrictions to the domain of a cubic? Are there maximums or minimums of a cubic function? Are there any holes, gaps, or asymptotes to worry about?

Quartic Functions Are there any restrictions to the domain of a polynomial to the fourth degree? Are there any maximums or minimums to worry about?

Summary the degree of a polynomial can give you a clue to the domain and range EvenOdd Domainall real numbers Range there will always be maximum or minimum quadratics: find the y value of the vertex and decide if it opens up or down others: use your graphing calculator all real numbers

Determine the domain and range of the following functions 1. y = 3x g(x) = 2x 2 +4x h(x) = (x-4)3 4. t(x) = 4x 4 - 6x 3 - 7

Radical Functions Is there a difference between even roots and odd roots? What are the domain restrictions for even radical? Odd radicals? Are their minimums or maximums in either type?

Rational Functions Note: assuming the numerator is a constant (for now) Is there anything that you can’t divide by? Is there any answer that you can never get by division?

Summary RadicalRational Domain Even all numbers greater than or equal to the radicand = 0 Odd all real numbers all real numbers except when the denominator = 0 Range Even all numbers greater than or equal to f(minimum domain value) Odd all real numbers all real numbers except 0

Determine the domain and range of the following functions 1. 2.