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
g
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?
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