A Hole in the Graph

more about rational function graphs

The Plug-Hole by flickr user ~~Tone~~

Graphing Rational Functions

Sketching (7 steps)

Step 1: Find the y-intercept (let x = 0)

Step 4: Find the vertical asymptotes by finding the roots of the denominator b(x).

Step 3: Find the roots of the function by finding the roots of the numerator a(x).

Step 2: Factor everything. (Use rational roots theorem if necessary.)

Graphing Rational FunctionsStep 5: Find the horizontal asymptotes by dividing each term in the function by the highest power of x, and take the limit as x goes to infinity. (Use the UNfactored form.)

You will find that, in general, there are three possible results:

i When [degree of numerator < degree of denominator] the horizontal asymptote is y = 0.

iii When [degree of numerator > degree of denominator] there is no horizontal asymptote; however there may be a slant asymptote or a hole in the graph.

ii When [degree of numerator = degree of denominator] the H.A. is the ratio leading coefficient of a(x)

leading coefficient of b(x)

Graphing Rational Functions

Sketching (7 steps)

Step 6: Determine the sign of the function over the intervals defined by the roots and vertical asymptotes. (Use the factored form.)

Step 7: Sketch the graph.

Graphing Rational Functions

Sketching: Example 1 of 4

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Sketch the graph of

Graphing Rational Functions

Sketching: Example 2 of 4

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Sketch the graph of

Graphing Rational Functions

Sketching: Example 3 of 4

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