Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible:
Vertical asymptotes x = -4, x = 5;
x-intercept (-2,0)
y=(x)/(x+4)(x-5)+ b
Put in y=0, x=-2, and solve for b.
To find a rational function that satisfies the given conditions, we need to first consider the vertical asymptotes and the x-intercept.
Vertical asymptotes indicate the values of x for which the function approaches infinity or negative infinity. In this case, we have two vertical asymptotes at x = -4 and x = 5.
To create these vertical asymptotes, we can use the factors of the denominator of the rational function. For x = -4, we need a factor of (x + 4), and for x = 5, we need a factor of (x - 5) in the denominator.
Next, let's consider the x-intercept at (-2, 0). An x-intercept is a point where the function crosses the x-axis. So, at x = -2, the function should equal 0.
To achieve this, we can create a factor of (x + 2) in the numerator.
Now, we can set up a rational function using these factors:
f(x) = (x + 2) / ((x + 4)(x - 5))
This rational function satisfies the given conditions. However, please note that there can be multiple correct answers, and the function could be written in different forms.