Algebra Functions

WARMUP Complete the table: x4 – 2x(x, y) 4 – 2(-1)(-1, 6)

3-8 Functions A function is a correspondence between two sets, D and R, that assigns to each member of D exactly one member of R. Real world example: Post Office: The cost of mailing a letter is a function of its weight – the heavier it is, the more it will cost to mail. There is a correspondence, cost to weight, given by a definite rule.

3-8 Functions Another example. Paul VI has a grade scale – a letter grade is a function of the numeric grade earned by the student. There is a correspondence, letter grade to numeric grade, given by a definite rule. Can you think of any other examples?

3-8 Functions You can think of functions as a machine, that you put something in, and get something out on the other side, based on rules inside the machine.

3-8 Functions National Library of Virtual Manipulatives: Check out the Function Machine… Another cool one: source.dspView&ResourceID=133

3-8 Functions Again, a function is a correspondence between two sets, D and R, that assigns to each member of D exactly one member of R.

3-8 Functions Mapping diagrams in book…

3-8 Functions The set D is the domain of the function. The range of the function is the is the set of all members of R assigned to at least one member of D. Note: Unless otherwise stated, domains and ranges in our book will be sets of Real numbers.

3-8 Functions So, an example of a rule for a function might be: “double the number.”

3-8 Functions The letters f, g, F, G, and occasionally , (Greek phi) are used to name functions. In the book you might see arrow notation: g: x 2x This is read “g, the function that assigns to x the number 2x”

3-8 Functions The graph of a function ƒ is the set of all points (x, y) such that x is in the domain of ƒ and the rule of the function assigns y to x. The values of a function are the members of it’s range. If g: x 2x then g assigns to 2 the value 4. Functional notation: write g(x) = 4

3-8 Functions f(2) = 4, read “the value of f at 2 is 4” or more commonly, “f of 2 is 4” In general: f(x) denotes the value of f at x BE CAREFUL: f(x) DOES NOT MEAN f multiplied by x!!!

3-8 Functions Domains and ranges. IMPORTANT: The domain of a function is the set of those real numbers for which the equation produces real numbers! What are the domains of the following:

3-8 Functions The range of functions are the values that can come out of the function: What are the ranges of the following functions:

3-8 Functions More practice… Homework