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Lana71 [14]
3 years ago
11

The rational function has a y-intercept of 7. What is the equation for this function?

Mathematics
1 answer:
Schach [20]3 years ago
0 0

Answer:

\large\boxed{f(x)=\dfrac{4}{x+2}+5}

Step-by-step explanation:

f(x)=\dfrac{a}{x-b}+c\\\\\text{We have}\\\text{(1) the vertical asymptote}\ x=-2.\ \text{Therefore}\ b=-2.\\\text{(2) the horizontal asymptote}\ y=5.\ \text{Therefore}\ c=5.\\\text{(3) the point (0, 7). Put the coordinates of the point to the equation}\\\text{of the function}\\y=\dfrac{a}{x-(-2)}+5\\\\7=\dfrac{a}{0+2}+5\qquad\text{subtract 5 from both sides}\\\\2=\dfrac{a}{2}\qquad\text{multiply both sides by 2}\\\\4=a\to a=4\\\\\text{Finally:}\\\\f(x)=\dfrac{4}{x+2}+5

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