P.O.D. Write the slope-intercept forms of the equations of the lines through the given point (2,1) & a)Parallel & b)Perpendicular to the line 4x – 2y = 3.

1.2 FUNCTIONS

Relation - a mapping, or pairing, of input values (Domain) to output values (Range). Ex. {(1,0),(1,2), (2,1), (2,3), (3,2), (3,4)} is a relation.

More examples of relations - Your name & your student ID # Time of day & temperature Radius and Area of a circle

Function -a type of relationship where each input is matched with exactly one output. *each ordered pair has a different x-coordinate

Would these coordinates come from a function?? Ex.{(1,0),(1,1),(2,1),(2,3), (3,2), (3,4)} NOT a function.

FunctionNot a Function

Vertical Line Test- if any vertical line is drawn so that it intersects the graph at one and only one point then it is a graph of a function.

FunctionNot a Function

“y as a function of x” -Means that the variable y depends on the variable x. -y is the dependent variable and x is the independent variable.

Testing for functions Algebraically 1) Solve the eq. for y 2) Make sure that for any given value of x there will only be only one value for y.

Ex. Determine whether the equation represents y as a function of x: 1) x 2 + y 2 = 8 2) x = y 3 - 5

FUNCTION NOTATION: *Functions are named by using a single letter: f, g, h, F, G, Ф, etc. Ex. f(x) “the value of function f at x” or “f of x”

*The ordered pair for a function is (x, f(x))  “f(x)” is basically the same as “y”, except “y” can be used in an equation that is not a function, unlike “f(x)”

EVALUATING FUNCTIONS: Let f(x) = 10 – 3x 2 find : a. f(2) b. f(-4) c. f(x – 1) Evaluating is simply substituting in a value or expression for x.

Piecewise-Defined Function A function defined by two or more equations over a specified domain

Absolute Value Function as a Piecewise-Defined Function

More examples of Piecewise Functions

Graph then evaluate the following: a. f(2) b. f(-4) c. f(5)

Implied Domains: The Domain of each function is all real numbers for which the function is defined. It describes all possible “inputs” of the function.

Evened-Root Functions Ex. 1 Ex. 2 Ex. 3

Rational Functions Ex. 1 Ex. 2