Find the equation of the function. (please explain so I understand)

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Find the equation of the function. (please explain so I understand)

Mathematics
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Hmm. A tricky one. I think I can help you, if you help me help you :) Based on whatever you've been doing at school, can you make a guess about what sort of function we might need to use? I can think of lots of examples, like sqrt(), tan(), 1/x, and so on. Any guesses?
Maybe even exponentials, like exp(-x) or something?

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I'm thinking ln or log function, not sure though
Okay, that's certainly sounds possible. Just to check though, is y=4 an asymptote? (i.e. the line gets closer and closer to 4 but doesn't touch it?)
that's what the graph I have looks like, so I'd say so
It looks like a rational function: \(y=\dfrac{ax+b}{cx+d}\). If it is, you can find out the values of a, b, c and d by examining the graph: begin with the horizontal asymptote. Because that is y=4, this means a/c=4, so take a=4 and c=1. All you need to do now is substituting (0,0) and (1,2) to find the values of b and d...
With logarithms you wouldn't get a horizontal asymptote...
After substituting (0, 0) and (1, 2), I got this:
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First, try (0, 0): \(0=\dfrac{0+b}{0+d}\), so \(\dfrac{b}{d}=0\), which means c=0.
Now try (1, 2): \(2=\dfrac{4 \cdot 1}{1+d}\), so \(1+d=\dfrac{4}{2}=2\), which means: \(d=1\). All in all we have: \(y=\dfrac{4x}{x+1}\). There could be othewr formulas, involving the exponential function.
Like \(y=4-a\cdot e^{-bx}\). Again, the values of a and b can be found by substituting (0, 0) and (1, 2).
thank you!! that actually helped a lot :)
YW! When I try the exponential function, I get (after substituting the points (0, 0) and (1, 2)): \(y=4-4e^{-x \ln 2}\) See image. It matches the specs, maybe even better, because the graph rises faster to the asymptote y=4. Looks more like your drawing imo.
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