Properties of Functions

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Presentation transcript:

Properties of Functions How are Functions Evaluated? Section 2.1 Properties of Functions

How are Functions Evaluated?

Does this Represent a Function? How are Functions Evaluated?

Identify the Domain and Range How are Functions Evaluated?

Find the Domain and Range for the Function below Solution: The domain includes only those values of x satisfying since the denominator cannot be zero. Using the methods for solving a quadratic inequality produces the domain Because the numerator can never be zero, the denominator can take on any positive real number except for 0, allowing y to take on any positive value except for 0, so the range is How are Functions Evaluated?

Find the Domain and Range for the Function below Solution: The domain includes only those values of x satisfying since the denominator cannot be zero. Using the methods for solving a quadratic inequality produces the domain Because the numerator can never be zero, the denominator can take on any positive real number except for 0, allowing y to take on any positive value except for 0, so the range is How are Functions Evaluated?

How are Functions Evaluated? Assessment Prompt #1 One’s do page 54 #7, 17, 27 Two’s do page 54 #5, 19, 25 Check each other’s work. Be ready to share out. How are Functions Evaluated?

How are Functions Evaluated? Substitution Given the function find each of the following. (a) (b) All values of x such that (a) Solution: Replace x with the expression x + h and simplify. (b) Solution: Set f (x) equal to − 5 and then add 5 to both sides to make one side equal to 0. Continued How are Functions Evaluated?

Substitution continued (b) Solution: Set f (x) equal to − 5 and then add 5 to both sides to make one side equal to 0. How are Functions Evaluated?

Are these graphs functions? How are Functions Evaluated?

How are Functions Evaluated? Assessment Prompt #2 One’s do page 55 #41, 49, 71 Two’s do page 55 #43, 47, 71 Check each other’s work. Be ready to share out. How are Functions Evaluated?

How are Functions Evaluated? Lesson Assignment Explain how to find f(250 + x) for the function f(x) = 3x -5. How are Functions Evaluated?

How are Functions Evaluated? Page 53-57 #4-32 every other even and #44-80 every other even Homework How are Functions Evaluated?