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MATH 1013 Chapter Notes -Asymptote, Graph Paper, Maxima And Minima


Department
Mathematics and Statistics
Course Code
MATH 1013
Professor
N/ A

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Summary of Curve Sketching
In this section, we will cover up a few general points that you need to remember when writing an
exam/midterm for any Math 1013 course at York University.
In order to sketch a graph, you will need:
Domain
X and Y-intercepts
Symmetry
Asymptotes
Intervals of Increase/Decrease
Local maximum/minimum
Concavity and Inflection points
Let us take a simple example:
   
The function can also be written as:
    
Domain:
To calculate the domain of the function, the denominator has to be equated to zero, i.e.
 
which in turn gives us:   
Hence, the domain D of   
X and Y-intercepts:
Let us begin by calculating the y-intercept. To calculate the y-intercept, simply calculate .
Since 
undefined, there is no y-intercept.
Next, to calculate the x-intercept, simply evaluate  .
 
 
 
 
Therefore, the x-intercept is x = 1.
Symmetry:
To determine the symmetry of a function, use the following general rules:
-   symmetric about the y-axis
-   symmetric about the origin
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