A rational function that passes through (0,0) and (4, 8/7) has the x-axis as a horiztonal asympotote. It also has 2 vertical asymptotes x=3, x=-3.
I understand that to set it up, it is
y= ax+b / (x+3)(x-3).
I don't understand how to solve for a and b.
To solve for the values of "a" and "b" in the rational function, we can use the given information and the points (0,0) and (4,8/7).
Let's start by using the point (0,0) to find the value of "b". Plug in the x-coordinate (0) and the y-coordinate (0) into the rational function:
0 = a(0) + b / (0+3)(0-3)
Simplifying this equation gives:
0 = b / (-3)(-3)
0 = b / 9
Since anything divided by zero is zero, we can conclude that "b" must be zero in order for the point (0,0) to lie on the graph. Therefore, we have found the value of "b".
Now, let's use the other given point (4,8/7) to find the value of "a". Plug in the x-coordinate (4) and the y-coordinate (8/7) into the rational function, and substitute the value of "b" we just found (which is 0):
8/7 = a(4) + 0 / (4+3)(4-3)
Simplifying this equation gives:
8/7 = 4a / 7
Now, cross-multiply and solve for "a":
8(7) = 4(7a)
56 = 28a
a = 56/28
a = 2
So, we have found the values of "a" and "b" in the rational function. The rational function that satisfies the given conditions is:
y = 2x / (x+3)(x-3)