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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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+4

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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+2

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

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