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 constants a and b in the rational function, you can use the given points that the function passes through: (0,0) and (4, 8/7).
Let's start by placing the first point (0,0) into the equation:
0 = a(0) + b / ((0+3)(0-3))
0 = 0 + b / (3)(-3)
0 = b / (-9)
b = 0
Now, let's place the second point (4, 8/7) into the equation:
8/7 = a(4) + b / ((4+3)(4-3))
8/7 = 4a + 0 / 7
8 = 4a
a = 8 / 4
a = 2
So, the rational function that satisfies the given conditions is:
y = (2x / (x+3)(x-3))
Therefore, the values of a and b in the function are a = 2 and b = 0.