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.

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