Thread: Finding the equation of a rational function.

I need help with this problem as soon as possible.

Suppose you have the function f(x)=2x+b
cx+d
This function is undefined at x=-4
3, the graph of this function strikes the x axis at 8 and the y axis at 1. What are the values for b,c and d?

I have no idea how to do any of this

I'm assuming you mean

Hints
If the function is undefined at , it usually means a division by zero takes place. *hint*hint

If it strikes the x axis at 8, that means when f(x)=0, x=8, i.e.:f(8)=0
And if it strikes the y-axis at 1, that means that at x=0, f(x)=1, i.e. f(0)=1

Substitute the values and use the hints.

I'm still not fully understanding this...ugh

Alright, you have :



You also know that a division per zero necessarily occurs in this function if , if and only if . You can reasonably assume that is not equal to zero since that would be really boring. And when a division per zero occurs, what happens ? The function is undefined.

Therefore, if the function is undefined at , the denominator is equal to , which means you have to solve

The graph of this function cuts the x-axis in , which means that when , . You then have .

The graph of this function cuts the y-axis in , which means that when , . You then have .

Let's resume all this :





, equivalent to

, equivalent to

______________________


Now I'll do a bit for you in this spoiler (don't click if you want to find by yourself) :

Spoiler:

means that

Therefore, the function becomes :



Now you know that , which means that

Therefore, the function becomes :



Remember that , so we have :



Now use one of the x-axis / y-axis values to substitute, isolate and solve .

You can solve for , therefore you can solve for , and the last variable remaining ( ) can be found by reverting to the original function and substituting the y-axis cut values.

I might have done some errors in the spoiler though, so don't just copy blindly.

Originally Posted by thisisnew

Suppose you have the function f(x)=2x+b
cx+d
This function is undefined at x=-4
3, the graph of this function strikes the x axis at 8 and the y axis at 1. What are the values for b,c and d?

I have no idea how to do any of this

when , cx + d = 0, hence

f(x) strikes x-axis at (8,0) and y-axis at (0,1)
hence ,
hence 16 + b = 0
b = -16
also ,
hence c(0) + d = 2(0) + b
0 + d = 0 + (-16)
d = -16
Since ,


c = -12

Ukorov, you can simplify a bit your work by clearly saying that , therefore getting rid of the part involving evaluation of . It makes it a bit shorter, and a lot cooler I find