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ACCURATE GRAPHING AND UNFAMILIAR FUNCTIONS

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1) Label your x-axis with the given interval 2) Enter function into Y1 and set xmin and xmax to interval, zoom 0 3) Create a table of values and plot those points on your graph 4) Find any relative extrema and plot on your graph 5) Determine the equation of any asymptotes and draw on your graph 6) Find any axes intercepts and plot on your graph 7) Draw the graph of the function, including all the points previously plotted 8) Make sure the y-axis reflects the range in the given interval 9) For trigonometric you need to determine period and amplitude Steps to Accurate Graphing

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Accurate Graphing: Familiar Functions What are some functions whose graphs you already know? Polynomials Exponential Trigonometric Reciprocal/Rational

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Step 1: Label you x-axis with the given interval

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Step 2: Create a table of values(use the table in your calculator) x-7-6-5-4-3-2012 y

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Plot the points from your table

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Step 3: Find any relative extrema, plot them (-1.5,10.25)Relative Minimum

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Step 4: Determine the equation of any asymptotes and draw them on the graph Quadratic Function None

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Step 5: Find any axes intercepts and plot them x-intercept (-4.7,0) x-intercept (1.7,0)

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Step 6: Draw the graph of the function Step 7: Make sure the y-axis reflects the range of the given interval

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x020406080100120140160180200 y

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What would the period of this function be? What would be the amplitude?

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Accurate Graphing: Unfamiliar Functions Graphing unfamiliar functions is done the same way as when graphing the functions whose shapes you know…..however, a calculator is necessary to determine the shape. Often if an unfamiliar function is a combination of two functions you know, then the new functions takes on some of the properties of the familiar functions

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Accurate Graphing: Unfamiliar Functions

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Step 1: Label you x-axis with the given interval

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x-5-4-3-212345 y Step 2: Create a table of values(use the table in your calculator)

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Plot points from table of values

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(1.44,1.88) Relative Minimum Step 3: Find any relative extrema, plot them

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Step 4: Determine the equation of any asymptotes and draw them on the graph Vertical Asymptote at x=0 Horizontal Asymptote y=0

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Step 5: Find any axes intercepts and plot on your graph This function has no axes intercepts

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Step 6: Draw the graph of the function, including all plotted points Step 6: Make sure the y-axis reflects the range of the given interval

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x0.5123456788.5 y

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What would the period of this function be? What would be the amplitude?

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Warm up Write the equation in vertex form of the quadratic equation that has been: 1. shifted right 7 and down 12 2. reflected across the x-axis and shifted.

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