Functions (but not trig functions!) Objectives: Be able to… -Identify, evaluate and find the domain of functions. -Determine where a graph is increasing, decreasing or constant -Find the extrema of a function -Determine if a function is even, odd or neither TS: Make decisions after reflection and review

Formal Definition A function, f, from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) and the set B contains the range (or the set of outputs).

Is it a function? What is the domain & range?

Is it a function? What is the domain & range? x 2 3 4 5 y 11 10 8 1

Is it a function?

Find the domain of each

Find the domain of each

Increasing, Decreasing or Constant Increasing Interval: For any x1 and x2 in the interval x1 < x2 implies f(x1) < f(x2) Decreasing Interval: For any x1 and x2 in the interval x1 < x2 implies f(x1) > f(x2) Constant Interval: For any x1 and x2 in the interval x1 < x2 implies f(x1) = f(x2)

Find the open intervals of x over which the functions are increasing, decreasing or constant. y=|x2 – 4|

Extrema (Absolute & Relative Maximums & Minimums) Using your calculator approximate the extrema for f(x) = -x3 + x Using your calculator approximate the extrema for Using your calculator approximate the extrema for y = |x – 3| + |x + 4| - |x+2|

Even & Odd Functions Even functions: Functions which have y-axis symmetry f(-x) = f(x) Odd Functions: Functions which have origin symmetry f(-x) = – f(x)

Test algebraically to see if each function is even, odd or neither Test algebraically to see if each function is even, odd or neither. Then verify graphically. g(x) = x3 – x 2) h(x) = x2 + 1 3) f(x) = x3 – 1

Closure: See if you can think of answers to these two questions. Find two non-polynomial even functions. They can’t both use the same parent. Draw a picture of an object that has both origin and y-axis symmetry. Can you make one that is a function?