Graph the Rational Function (-x+2)/(x + 4)

    You might wish to review how to take notes on a computer.

An Examples of the Sketching Rational Functions

    See the computer sketch

To sketch a rational function:
· Rewrite it by factoring
identify the linear, quadratic, and reciprocal factors.
· Rewrite it by division
to identify curve shifting.
· Plot zeros
-- identified by the real roots of linear or quadratic factors.
· Mark vertical asymptotes
-- the roots of denominators of the reciprocal factors.
· Check for discontinuities or holes
-- identified by identical factors on the "top" and "bottom" of the fraction.
· Mark other asymptotes
-- the nonremainders part of the quotient from the long division.
· Determine sign in intervals
-- using the positiveness or negativeness of each factor.
· Find end behaviors
-- the "winner in the battle of the top against the bottom."
· Set the derivative equal to 0, solve to find x values where the slope is zero
-- to give the x values of relative maximums, relative minimums, flat spots, discontinuities. (Not shown in these examples.)
· Find end behaviors
-- the "winner in the battle of the top against the bottom."
· Sketch curve.

Click on the image to see an enlargement.

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