3.2 Functions (Day 1) Today’s Date: 11/1/17

Functions Relation: any set of ordered pairs (x, y) Domain: set of x-values Range: set of y-values Function: relation where x-values don’t repeat On a graph, it passes the vertical line test Written:

Ex 1) Relation: {(–1, 0), (0, –1), (1, 0)} Domain: { –1, 0, 1} Range: { –1, 0} Function? YES! (x’s don’t repeat) Ex 2) Is the relation a function? p = {(x, y) │ x = –2} No! Fails vertical line test! Don’t repeat yourself!

Finding the domain & range of an equation: Domain: look for any restrictions on x (y must be real) x under radical x in denominator of fraction

Finding the domain & range of an equation: Range: look for any restrictions on y (using known domain) Draw a quick sketch if need to or use graphing calculator

Ex 3) Find domain & range of Range: y is only positive (square of negative is positive) All Real Numbers Interval Notation:

Ex 4) Find D & R of Domain: term under radical must be ≥ 0 Range: under radical ≥ 0

Find: Ex 5) Ex 6) Ex 7) Ex 8)

Homework #303 Pg. 178 1 – 43 odd

3.2 (Day 2) Difference Quotient & Graphs of Functions Today’s Date: 11/1/17

Difference Quotient (used in Calculus to study tangent lines to curves)

Ex 1) Find the difference quotient of

Ex 2) Sketch the graph of Pass the vertical line test? Yes! Function! -2 -1 1 2 3 4 5 │-2 – 2│ │-1 – 2│ │0 – 2│ │1 – 2│ │2 – 2│ │3 – 2│ │4 – 2│ │5 – 2│ 4 3 2 1 Pass the vertical line test? Yes! Function!

Ex 3) Determine if function: No! It doesn’t pass the vertical line test.

Greatest Integer Function: Greatest integer ≤ x AKA Floor Function

Ex 4) Graph It’s a function, so must pass vertical line test Plug in positive decimal values ≥ 1 to get a feel then fill in pattern, including negatives It’s a function, so must pass vertical line test y x x y 1.0 1.2 1.9 2.0 2.2 2.9 3.0 1 2 3

Homework #304 Pg. 179 45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even