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

66)D: (-∞, ∞ ) R: y ≥ 1 70) A = (√3/4)s 2 76)a. x = indep, y = dep b. [7, 12] U [1,6] c ; $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 Functions Finding 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?

Increasing Functions Moving from LEFT to RIGHT a function is INCREASING i f the y- value increases as the x- value increases (graph goes up)

Decreasing Functions Moving from LEFT to RIGHT a function is DECREASING i f the y-value decreases as the x-value increases (graph goes down)

Constant Functions Moving from LEFT to RIGHT a function is CONSTANT i f 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 Minimum The 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 Maximum The 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) 1) Graph the function 2) 2) 2 nd  Calc  Minimum 3) 3) LB? Move cursor left of min. then press Enter 4) 4) RB? Move cursor right of min. then press Enter 5) 5) Guess? press Enter

Calc Key strokes To find relative maximum: 1) 1) Graph the function 2) 2) 2 nd  Calc  Maximum 3) 3) LB? Move cursor left of max. then press Enter 4) 4) RB? Move cursor right of max. then press Enter 5) 5) Guess? press Enter

Example The temperature, y, of a certain city can be approximated by the model y =0.026x 3 – 1.03x x+34 where x = 0 corresponds to 6am. Approximate the max & min temps using a calc.

Even Functions A function is even if its graph is symmetric with respect to the y-axis OR f(-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) = x #1 #2

Odd Functions A function is odd if its graph is symmetric with respect to the origin OR f(-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) = x 3 – x #1 #2