p.o.d. using your calculator find the domain and range of: a) b) c)
TRANSCRIPT
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P.O.D. Using your calculator find the domain and range of:a)b)
c)
9)( xxg
23)( xxf
7
5)(
x
xxh
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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.
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1.3 Graphs of FunctionsFinding Domain, Range,
increasing & decreasing intervals, relative
maximum & minimum
values
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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)
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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)
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Increasing FunctionsMoving from LEFT to RIGHT a function is INCREASING if the y-value increases as the x-value increases (graph goes up)
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Decreasing FunctionsMoving from LEFT to RIGHT a function is DECREASING if the y-value decreases as the x-value increases (graph goes down)
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Constant FunctionsMoving from LEFT to RIGHT a function is CONSTANT if the y-value equals the x-value (graph is horizontal)
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Where is the function increasing or decreasing?
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Relative Minimum or
Relative Maximum
(*also called “Extrema”)
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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.
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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.
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Relative “Extrema”
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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
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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
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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.
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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.)
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Even Functions Examples
h(x) = x2 + 1
#1
#2
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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.)
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Odd Functions Examples
f(x) = x3 – x
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#2