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For certain constants \(a,b,c,\) and \(d,\) the graph of the function \(y = \frac{ax + b}{cx + d}\)
has 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 25, 2020
 #3
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I just did a long answer and then lost it.

So I will give you the short version.

This is just a hyperbola.

You do not even need to worry about all those letters.

Just solve it as a hyperbola

 

\(y-k=\frac{k}{x-h}\\ y+3=\frac{k}{x-7}\\\)

 

Solve for k by subbing in (0,6)

then you have the equation. So you can easily find the x-intercept.

 

If you want to you can rearrange the formula to solve for a, b, c and d

 Apr 26, 2020

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