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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