How do we describe the Domain and Range of a function? Do Now: What are all values that we can plug into the equation x3 y 2 x 4 What is the Domain of a function? • The domain of a function is the set of every value that can be plugged into the function. • In the Do Now, the Domain is the set of all real numbers except ±2 • This can be written as R/{±2} What is the Range of a function? • The range is the set of numbers that can come out of the function. • Often it is more difficult to find the range than it is to find the domain Type Example Domain Range Linear y=2x-1 All real All real Quadratic y=x2-4 y=-2x2+4x+5 All real y≥-4 y≤5 Cubic y=x3+6 All real All real Absolute Value y= 2x-3 All real y≥0 All real except x=-5 x≤10 y≥0 Rational Functions with radicals 3x 1 y x5 y 10 x Examples • Determine the largest possible domain for each function 3x 1 f (x) 2 x 3x 4 7x g(x) 5 2x h(x) 2x 4 Try on your own • Determine the largest possible domain and range for each function 2 f (x) x 10 3 g(x) x 8x 15 2 h(x) 3 4 x Summary/HW • How does the type of function impact its domain and range? • HW: pg 152-3, 1-21 odd

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# How do we describe the Domain and Range of a function?