Sketch the graph of each of the following rational functions. Explicitly state the values asked for below and show how you determined those values. a) the equations of any horizontal asymptotes b) the equations of any vertical asymptotes c) any non-permissible values as a coordinate (other than asymptotes) y=1x−3+2

Question

Sketch the graph of each of the following rational functions. Explicitly state the values asked for below and show how you determined those values.  a) the equations of any horizontal asymptotes  b) the equations of any vertical asymptotes  c) any non-permissible values as a coordinate (other than asymptotes)  y=1x−3+2

Keely House · Accepted Answer

Step 1  a) Horizontal asymptote is as follow:  limx→∞(2+1x−3)=2  limx→−∞(2+1x−3)=2  Therefore, the horizontal asymptote is y=2  b) y=1x−3+2  Simplify:  y=1+2(x−3)x−3  The denominator is x−3  x−3=0⇒x=3  The vericle asymptote is x=3  c) And non permissible value is any value in [3, ∞)  Let x=4  y=14−3+2=3  The non permissible value as coordinate is (4, 3)  The graph is as follow with asymptotes and non permissible co-ordinates :

Sketch the graph of each of the following rational functions.

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New Questions in Calculus 1