# the rational function has a y-intercept of 7. what is the equation for this function

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2. If all we know is the point (0,7) then it must be of the form

y = a(x-7) * ...

where ... is some fraction involving x-stuff.

I cannot access files on your C: drive ...

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3. the vertical asymptote is at -2 and the horizontal asymptote is at 5

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4. so, y = 5(x-7)/(x+2)

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5. thank you so much!

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6. could u show me how u got it step by step though

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7. the vertical asymptote means you have (x+2) in the bottom
the zero means you have (x-7) in the top
The top and bottom have equal degree, so the y-asymptote is the ratio of the coefficients of the highest power of x. The fraction (x-7)/(x+2) has a horizontal asymptote at y=1. So, multiply by 5.

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8. ok,thank you so much

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9. I can give you an answer for them, but they may not be correct.
1. y = (5x+14)/(x+2) You can graph this in mathway if you're not sure

2. It's a direct variation and the function is y = 3x. You can still check with mathway

3. It's shifted to the left by 6 units, and is stretched by 5 units (Not really sure about this one tbh)

4. 500 = C (n + 5)
500 = 20 (n + 5)
20 (n + 5) = 500
20n + 100 = 500
20n = 400
n = 20

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10. Y=5
X=-2
K=5
Y=a/(x+2) +5
Since x is -2 it will be (x+2)
Now we need to find the A value
The y Intercept is at (0,7)
Substitute 0 and 7 for x and y
7= a/(0+2) +5
-5 both sides
2=a/0+2
0+2 is 2
2=a/2
Multiply both sides by 2
2 × 2 is 4
A= 4
The equation is
Y=4/(x+2) +5

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11. formula i used
y=a/(x-h) +k
vertical asymp x=-2 and/or h=-2
horizontal asymp y=5 and/or k=5

y=a/x-(-2) +5
plug in the (0,7) to find a
7=a/0+2 +5
subtract 5
2= a/2 multiply 2 to cancel out the division
a=4
plug everything in
y= 4/x+2 +5
check desmos

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