This

**preview**shows page 1. to view the full**4 pages of the document.**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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