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A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0).

 

PART A: Let f be of the form

 

                       f(x)=(ax+b)/(x+c)

 

Find an expression for f(x).

 

PART B: Let f be of the form

 

                       f(x)=(rx+s)/(2x+t)

 

Find an expression for f(x).

 

Thanks!

AnonymousConfusedGuy  Dec 18, 2017
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2+0 Answers

 #1
avatar+86649 
+3

A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0). PART A: Let f be of the form

                       f(x)=(ax+b)/(x+c)

                       Find an expression for f(x).

 

Since we have a vertical asymptote at x = 3, c  = - 3.....and since we have a horizontal asymptote at y  = -4, a  = -4......and since we have an  x intercept at (1,0), we can solve this for b ⇒  -4(1)  +  b =  0 ⇒  b  = 4......here's the graph : https://www.desmos.com/calculator/1pmoaiuapl

 

PART B: Let f be of the form

                       f(x)=(rx+s)/(2x+t)

Find an expression for f(x).

 

Since the vertical asymptote is at 3 , we can solve this for t.....2(3) + t  = 0 ⇒  t  = -6

And since the horizontal asymptote is at -4, r  = -8

And since we have an x intercept at (1,0), we can solve this for s......-8(1) + s  = 0 ⇒  s  = 8

Here's a graph : https://www.desmos.com/calculator/gyqo2l6jdl

 

 

cool cool cool

CPhill  Dec 18, 2017
 #2
avatar+1050 
+2

Thanks!

AnonymousConfusedGuy  Dec 18, 2017

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