ok I am at a total loss here.
I have a graph with the points (0,-3) (0,-5) (3,-2) (5,-7)
with vertical asymptote of (6,1)
I have to find the rational function. where do I start?
To find the rational function that corresponds to the given points, you can follow these steps:
1. Start by determining the degree of the rational function. Since the given points are not collinear, the rational function will have at least a degree of 1.
2. Use the given vertical asymptote to determine the degree of the denominator. In this case, the vertical asymptote is at x = 6. So, the denominator should include a factor of (x - 6).
3. Set up the general form of the rational function:
f(x) = (nominator) / (denominator)
4. Plug in the given points to form a system of equations. Substitute the x and y values of each point into the rational function.
Taking the given points (0,-3), (0,-5), (3,-2), (5,-7), we can set up the following equations:
For point (0, -3):
-3 = (nominator) / (denominator)
For point (0, -5):
-5 = (nominator) / (denominator)
For point (3, -2):
-2 = (nominator) / (denominator)
For point (5, -7):
-7 = (nominator) / (denominator)
So now, we have a system of equations that we can solve.
5. Solve the system of equations. To do this, you can use any method you prefer, such as substitution or elimination. After solving, you will obtain the values for the nominator and denominator.
6. Once you have the values for the nominator and denominator, you can write the final rational function in the form:
f(x) = (nominator) / (denominator)
By following these steps, you can find the rational function that corresponds to the given points.