+0  
 
+3
47
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avatar+1063 

For certain constants a, b, c, and d, the graph of the functionhas a vertical asymptote of x = 7, a horizontal asymptote of y = -3, and a y-intercept of (0,6). Find the x-coordinate of the x-intercept.

 Apr 18, 2020
 #1
avatar+20812 
+1

To have a vertical asymptote of x = 7, the function needs a factor of (x - 7) in the denominator.

The function then can look like this:  f(x)  =  a / (x - 7)  for any non-zero value of a.

 

This function will have a horizontal asymptote at y = 0.

For this function to have a horizontal asymptote of y = -3, the function can be modified to be:  f(x)  =  a / (x - 7) - 3.

 

Rewriting the function, using the common denominator:  f(x)  =  [ -3x + (21 + a) ] / (x - 7)

Since the y-intercept is (0,6):                                              6    =   (21 + a) / -7

Solving for a:                                                                         a  =  -63

 

The function is now:  f(x)  =  (-3x - 42) /(x - 7)

 Apr 18, 2020

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