ACCURATE GRAPHING AND UNFAMILIAR FUNCTIONS

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 Accurat

e Graphin

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Accurate Graphing: Familiar Functions

What are some functions whose graphs you already know?

PolynomialsExponentialTrigonometricReciprocal/Rational

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

Step 2: Create a table of values(use the table in your calculator)

x -7 -6 -5 -4 -3 -2 -1 0 1 2y

Plot the points from your table

Step 3: Find any relative extrema, plot them

(-1.5,10.25)Relative Minimum

Step 4: Determine the equation of any asymptotes and draw them on the graph

Quadratic FunctionNone

Step 5: Find any axes intercepts and plot them

x-intercept (-4.7,0) x-intercept (1.7,0)

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

x 0 20

40

60 80

100

120

140

160

180

200

y

What would the period of this function be?

What would be the amplitude?

Accurate Graphing: Unfamiliar FunctionsGraphing 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

Accurate Graphing: Unfamiliar Functions

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

x -5 -4 -3 -2 -1 1 2 3 4 5y

Step 2: Create a table of values(use the table in your calculator)

Plot points from table of values

(1.44,1.88) Relative Minimum

Step 3: Find any relative extrema, plot them

Step 4: Determine the equation of any asymptotes and draw them on the graph

Vertical Asymptote at x=0

Horizontal Asymptote y=0

Step 5: Find any axes intercepts and plot on your graph

This function has no axes intercepts

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

x 0 .5 1 2 3 4 5 6 7 8 8.5y

What would the period of this function be?

What would be the amplitude?