Sketch the graph of
id="TexFormula1" title="f(x) = \frac{x - 3}{x + 4 } " alt="f(x) = \frac{x - 3}{x + 4 } " align="absmiddle" class="latex-formula">
1 answer:
First find any vertical asymptotes:
Any x-values which make the denominator equal 0
---> x+4 = 0 -----> x = -4
Draw a vertical dotted line along x = -4
Next find any horizontal asymptotes:
A y-value that function approaches as x gets very, very large
Plug in x = 1000, then x = 1000,000. You will see the y-value get very,very close to 1.
In general if the exponents of top/bottom are equal, then the horizontal asymptote is the ratio of the leading coefficients.
Draw a horizontal dotted line along y= 1
Next pick 4 x-values, two on either side of the vertical asymptote.
x = 0 , x = -2, x = -8, x = -6
Plot the 4 points ----> (0,-3/4) , (-2,-5/2), (-6,9/2) , (-8,11/4)
Notice 2 points will be separated from the other 2 by the dotted lines.
For each pair of points, Draw a curved line through them so they approach but NOT cross the dotted lines.
Any x-values which make the denominator equal 0
---> x+4 = 0 -----> x = -4
Draw a vertical dotted line along x = -4
Next find any horizontal asymptotes:
A y-value that function approaches as x gets very, very large
Plug in x = 1000, then x = 1000,000. You will see the y-value get very,very close to 1.
In general if the exponents of top/bottom are equal, then the horizontal asymptote is the ratio of the leading coefficients.
Draw a horizontal dotted line along y= 1
Next pick 4 x-values, two on either side of the vertical asymptote.
x = 0 , x = -2, x = -8, x = -6
Plot the 4 points ----> (0,-3/4) , (-2,-5/2), (-6,9/2) , (-8,11/4)
Notice 2 points will be separated from the other 2 by the dotted lines.
For each pair of points, Draw a curved line through them so they approach but NOT cross the dotted lines.
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