- Is the graph symmetric with respect to: the x-axis, the y-axis, or the origin
For y axis, determine if f(x) equal to f(-x). For the origin, determine if -f(x) = f(x). For the x axis, determine if each value of x gives pairs of values of y above and below the x axis by the same magnitude.
- Find all vertical/horizontal asymptotes
Vertical: Are there any values of x which would make the function undefined? Or, if it was a single fraction, any values that would make the denominator zero?
Horizontal: Determine the limits as x->infinity or minus infinity.
- Find the x-coordinates of each point at which y has a relative maximum or minimum'
- Find the x-coordinate of each point of inflection
Find f'(x) and f''(x). Where f'(x)=0 it is a maximum or minimum, then use f''(x) for that value to determine its nature.
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