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# Function notations for the graphs are f(x) = 2 + 20/x-3 and g(x) = -3 + 32/2x+4

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Two graphs are drawn, and the function notations for these graphs are f(x) = 2 + 20/x-3 and g(x) = -3 + 32/2x+4

a. Give the formule for the vertical and horizontal asymptotes of the graph of function f

b. Give the formule for the vertical and horizontal asymptotes of the graph of function g

c. Which graph belongs to function f and which belongs to function g?

d. Jasper has drawn the graph for a fractional function. His graph has the line y = -3 as the horizontal asymptote and the line x = 4 as the vertical asymptote. Give a possible function notation for Jasper's graph. Jun 7, 2019

#1
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Assuming that     $$f(x)\ =\ 2+\frac{20}{x-3}$$     and     $$g(x)\ =\ -3+\frac{32}{2x+4}$$

 a.__ $$y\ =\ f(x)\\~\\ y\ =\ 2+\frac{20}{x-3}$$ y  is undefined when  x - 3 = 0  so there is a vertical asymptote at  x = 3 $$y-2\ =\ \frac{20}{x-3}\\~\\ (x-3)(y-2)\ =\ 20\\~\\ x-3\ =\ \frac{20}{y-2}$$ x  is undefined when  y - 2 = 0  so there is a horizontal asymptote at  y = 2 The equations for the vertical and horizontal asymptotes of the graph of  f(x)  are:   x = 3   and   y = 2 b. $$y\ =\ g(x)\\~\\ y\ =\ -3+\frac{32}{2x+4}$$ y  is undefined when  2x + 4 = 0  so there is a vertical asymptote at  x = -2 $$y+3\ =\ \frac{32}{2x+4}\\~\\ (2x+4)(y+3)\ =\ 32\\~\\ 2x+4\ =\ \frac{32}{y+3}$$ x  is undefined when  y + 3 = 0  so there is a horizontal asymptote at  y = -3 The equations for the vertical and horizontal asymptotes of the graph of  g(x)  are:   x = -2   and   y = -3 c. Here is a graph:  https://www.desmos.com/calculator/7zrrangdvv (Note you can hide or show  f(x) or g(x)  and its asymptotes by clicking the circles beside the function.) Graph 2  belongs to  f(x)  and  graph 1  belongs to  g(x) . d. A possible function is:     $$f(x)\ =\ -3+\frac{1}{x-4}$$_
Jun 7, 2019
#2
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Thank you, your answer is very clear and I kinda do understand what you're doing. I'm just not really good at things concerning functions and graphs haha oops.

Jun 7, 2019