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Answer:
The graph has a removable discontinuity at x=-2.5 and asymptoe at x=2, and passes through (6,-3)
Step-by-step explanation:
A rational equation is a equation where
where both are polynomials and q(x) can't equal zero.
1. Discovering asymptotes. We need a asymptote at x=2 so we need a binomial factor of
in our denomiator.
So right now we have
2. Removable discontinues. This occurs when we have have the same binomial factor in both the numerator and denomiator.
We can model -2.5 as
So we have as of right now.
Now let see if this passes throught point (6,-3).
So this doesn't pass through -3 so we need another term in the numerator that will make 6,-3 apart of this graph.
If we have a variable r, in the numerator that will make this applicable, we would get
Plug in 6 for the x values.
So our rational equation will be
or
We can prove this by graphing
y = 5 x +3 is the final equation when y = 5 x 3 units up
<u>Step-by-step explanation:</u>
In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.
Here we have , y=5x . Function y = 5x is a straight line passing through origin and having a slope of 5 . Now we need to increment this function 3 units up i.e. y = 5x + 3 , This a straight line passing through x-axis at and y-axis at 3. For your reference , following graph of y= 5x and y = 5x + 3 is attached .
