1.2 FUNCTIONS

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 FUNCTION

S

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.

Function Not 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.

Function Not 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 Algebraically1) Solve the eq. for y2) 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) x2 + y2 = 82) x = y3 - 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 – 3x2 find :

a. f(2)b. f(-4)c. f(x – 1)

Evaluating is simply substituting in a value or expression for x.

Piecewise-Defined FunctionA 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 FunctionsEx. 1

Ex. 2

Ex. 3

12 xxF )(

3)( 2 xxg

4 25)( xxh

Rational FunctionsEx. 1

Ex. 2

))(()(

212

xxxF

432)(

xx

xxG