Standard transformations can be used to help graph rational functions of the form f(x)=frac{A}{Bx-C}+D Explain how the parameters A, B, C, and D relate to the graph of the rational functions.

Tolnaio 2020-12-15 Answered
Standard transformations can be used to help graph rational functions of the form f(x)=ABxC+D Explain how the parameters A, B, C, and D relate to the graph of the rational functions.
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svartmaleJ
Answered 2020-12-16 Author has 92 answers

Step 1 Conclude function f(x) given: Has a vertical asymptote at x=CB Has a horizontal asymptote at y=D Step 2 Additionally, we may conclude that: If Cq0, the function will have a y-intercept at f(0)=AC+D If Dq0, we find the x-intercept as ABxC+D=0 which we solve for x to obtain x=CDABD The function will have a domain of (,CB)(CB,) If A>0,the function will decreas eonitsdoma, if A<0, the function will increase on its domain The end behavior of the function is yD as y ± Finally, the graph of f(x) is obtained from g(x)=1x by the following transformation: 1x basic graph 1xCB translate CB units to the right AB1xCB vertically stretch by a factor of AB AB1xCB+D translate D units up Simplifying the last exprexxion will result in the formula for f(x) aas given.

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