Assume the function has only one x-intercept at the origin, and the point marked on the graph is located at (6,-3/5). The asymptotes are x=-4 and x=5. give the formula as a reduced rational function.
y = ax / (x+4)(x-5)
Now just plug in your point to find a:
-3/5 = a*6 / 10*1
a = -1
y = -x/((x+4)(x-5))
To find the formula of a rational function with the given properties, we can start by considering the x-intercept at the origin. Since the x-intercept is at (0, 0), we know that the rational function has a factor of x in both the numerator and the denominator.
The formula of the rational function can be written as:
f(x) = (x - a)/(x - b)
where a is the value of the x-intercept and b is the value of the other asymptote.
In this case, the x-intercept is at (0, 0), so we have a = 0. The other asymptote is x = -4 and x = 5, so b can be either -4 or 5. We can choose either one.
Let's assume b = -4.
Now we can write the rational function as:
f(x) = (x - 0)/(x - (-4))
Simplifying the expression, we get:
f(x) = x/(x + 4)
So the formula of the reduced rational function with the given properties is f(x) = x/(x + 4).
To find the formula of a reduced rational function given the information provided, we need to consider the x-intercept, the point on the graph, and the vertical asymptotes.
First, since the function has only one x-intercept at the origin, we know that the numerator of the rational function would be the constant zero, since the function crosses the x-axis at (0,0).
So far, the rational function can be written as:
f(x) = 0/(x - h)
Next, let's consider the point marked on the graph located at (6,-3/5). This point must lie on the graph of the function. So, we can substitute this point into the equation to find the value of h.
Using the point (6,-3/5), we have:
-3/5 = 0/(6 - h)
Since the numerator is zero (as we discussed earlier), this equation simplifies to:
0 = 0
As this equation is always true for any value of h, it means that it does not provide any constraint on the value of h. Therefore, we can choose any value of h that satisfies the vertical asymptotes.
Given that the asymptotes are x = -4 and x = 5, we can choose any value of h between -4 and 5.
Let's choose h = 0.5. Keep in mind that this is just an example, and other valid choices can be made.
Now, we can write the equation of the reduced rational function as:
f(x) = 0/(x - 0.5)
Simplifying further, we obtain the final reduced rational function as:
f(x) = 0
Therefore, the formula of the reduced rational function, given the provided information, is f(x) = 0.