This is an analytical tutorial on rational functions to further understand the properties of the rational functions and their graphs. The examples have detailed solutions in this page, the matched exercises have answers here.
whose graph has a y intercept at (0 , -1) and has a vertical asymptote at x = 2.
Solution to Example 1:
The graph has y intercepts at (0 , -1) , you can write
f(0) = -1
Which leads to the equation
-1 = 2 / c
Solve the above equation for c.
c = -2
The vertical asymptote is given by the zero(s) of the denominator of the equation of the function. A vertical asymptote at x = 2 means that the denominator is equal to zero at x = 2. This leads to
2b + c = 0
Substitute -2 for c
2b - 2 = 0
and solve for b.
b = 1.
The equation of f is given by
f(x) = 2 / (x -2)
Check answer graphically. Below is shown the graph of f obtained. Check the y intercept and the vertical asymptote.