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Steps for graphing a function on Cartesian Coordinates System

Posted in Math Theory by Lia on 11/20/2011


To see the implementation of those steps look to the way Problem 10 – Solution and Problem 16 – Solution are done.


Step 1/5: Variation Table (VT) for the domain in which f(x) is defined.

1.1 Finding the values for the variable’s x limits for which the function is defined and adding the results to VT.

1.2 Finding the values for f(x) at x limits and adding the results to VT.


 Step 2/5:  Finding other (x, f(x)) points necessary  for graphing the function.

2.1 Finding the roots for  f(x) = 0 and adding the results to VT.

2.2 Finding the value of  f(x) when x = 0 and adding the result to VT.

2.3 Finding the roots for f{prime}(x) = 0 and adding the results to VT.

2.4 Finding the roots of f{prime}{prime}(x) = 0 and adding the results to VT. (This point is usually done when there is not enough data to graph the function.)


Step 3/5:  Finding the asymptotes. 

3.1 Oblique or slant asymptote has the form:

g(x) = ax + b

3.2 Horizontal asymptote has the form:

g(x) = b

3.3 Vertical asymptote has the form:

x = c

Where a, b and c are constants.


Step 4/5:  Finding the signs and direction of the function in between the (x, f(x)) points  found at Steps 1 and 2.

4.1 Finding the signs (plus or minus) for f{prime}(x), on the defined interval, and adding the results to VT. 

4.2 Finding the signs (plus or minus) for f{prime}{prime}(x), on the defined interval,  and adding the results to VT.

4.3 Adding {}{nearrow}{} (the function is going up) and {}{searrow}{} (the function is going down) on (x) row in VT.


Step 5/5:  Drawing the graph on the Cartesian Coordinates System following the values you input in VT.

5.1  If any asymptotes, they should be drawn  first.

5.2  Place the set points (x, f(x)) shown on VT, in the appropriate location, on the Cartesian Coordinates System.

5.3 Graph the function f(x).





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