## alexrobin13 one year ago Find the equation of the function. (please explain so I understand)

1. alexrobin13

|dw:1442524295814:dw|

2. anonymous

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?

3. anonymous

Maybe even exponentials, like exp(-x) or something?

4. alexrobin13

I'm thinking ln or log function, not sure though

5. anonymous

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?)

6. alexrobin13

that's what the graph I have looks like, so I'd say so

7. ZeHanz

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...

8. ZeHanz

With logarithms you wouldn't get a horizontal asymptote...

9. ZeHanz

After substituting (0, 0) and (1, 2), I got this:

10. ZeHanz

First, try (0, 0): $$0=\dfrac{0+b}{0+d}$$, so $$\dfrac{b}{d}=0$$, which means c=0.

11. ZeHanz

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.

12. ZeHanz

Like $$y=4-a\cdot e^{-bx}$$. Again, the values of a and b can be found by substituting (0, 0) and (1, 2).

13. alexrobin13

thank you!! that actually helped a lot :)

14. ZeHanz

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.