Use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = (−x2 − 3x − 1)/(x − 2)
Use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = (−x2 − 3x − 1)/(x − 2)
Chapter9: Quadratic Equations And Functions
Section9.7: Graph Quadratic Functions Using Transformations
Problem 361E: Graph the quadratic function f(x)=x2+4x+5 first using the properties as we did in the last section...
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Question
Use a graphing utility to graph the function and determine the slant asymptote of the graph analytically. Zoom out repeatedly and describe how the graph on the display appears to change. Why does this occur? f(x) = (−x2 − 3x − 1)/(x − 2)
Expert Solution
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Step 1
The given function is .
We have to:
(i) To draw The sketch of the curve.
(ii) To find the slant asymptote of the curve.
(iii)Why does the slant asymptote occur?
Step 2
The given function is .
To find the slant asymptote we will divide this rational function and then, using the quotient, we will get the equation of the slant asymptote.
Since,
The quotient is -x - 5. Thus, the equation of the slant asymptote is .
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