P.O.D. Using your calculator find the domain and range of:a)b)

c)

9)( xxg

23)( xxf

7

5)(

x

xxh

66)D: (-∞, ∞ ) R: y ≥ 170) A = (√3/4)s2

76)a. x = indep, y = dep b. [7, 12] U [1,6] c. 11.575; $11,575 monthly revenue for May d. 4.63; $4630 for Nov. e. they are approx. equal d. 4.63; $4630 for Nov.

1.3 Graphs of FunctionsFinding Domain, Range,

increasing & decreasing intervals, relative

maximum & minimum

values

DOMAIN of a Graph

Look at how far LEFT and/or RIGHT the graph extends (describes all possible inputs or x-coordinates on the graph)

RANGE of a Graph

Look at how far UP and/or DOWN the graph extends (describes all possible outputs or y-coordinates on the graph)

Ex.1 Domain & Range?

Function?#1 #2

Increasing FunctionsMoving from LEFT to RIGHT a function is INCREASING if the y-value increases as the x-value increases (graph goes up)

Decreasing FunctionsMoving from LEFT to RIGHT a function is DECREASING if the y-value decreases as the x-value increases (graph goes down)

Constant FunctionsMoving from LEFT to RIGHT a function is CONSTANT if the y-value equals the x-value (graph is horizontal)

Where is the function increasing or decreasing?

Relative Minimum or

Relative Maximum

(*also called “Extrema”)

Relative MinimumThe point(s) on the graph which have minimum y values or second smallest coordinates “relative” to the points close to them on the graph.

Relative MaximumThe point(s) on the graph which have maximum y values or second largest coordinates “relative” to the points close to them on the graph.

Relative “Extrema”

Calc Key strokes To find relative minimum:1) Graph the function2) 2ndCalcMinimum3) LB? Move cursor left of

min. then press Enter4) RB? Move cursor right

of min. then press Enter5) Guess? press Enter

Calc Key strokes To find relative maximum:1) Graph the function2) 2ndCalcMaximum3) LB? Move cursor left of

max. then press Enter4) RB? Move cursor right of

max. then press Enter5) Guess? press Enter

ExampleThe temperature, y, of a certain city can be approximated by the modely =0.026x3 – 1.03x2+10.2x+34 where x = 0 corresponds to 6am. Approximate the max & min temps using a calc.

Even FunctionsA function is even if its graph is symmetric with respect to the y-axis

ORf(-x) = f(x) for all x in the domain of f. (i.e. f(3) = f(-3), f(2)=f(-2),etc.)

Even Functions Examples

h(x) = x2 + 1

#1

#2

Odd FunctionsA function is odd if its graph is symmetric with respect to the origin

ORf(-x) = -f(x) for all x in the domain of f. (i.e. f(-3) = -f(3), f(-2) = -f(2),etc.)

Odd Functions Examples

f(x) = x3 – x

#1

#2