Expression: f(x) = [x - 4] / [x^2 + 13x + 36].
The vertical asympotes is f(a) when the denominator of f(x) is zero and at least one side limit when you approach to a is infinite or negative infinite.
The we have to factor the polynomial in the denominator to identify the roots and the limit of the function when x approachs to the roots.
x^2 + 13x + 36 = (x + 9)(x +4) => roots are x = -9 and x = -4
Now you can write the expresion as: f(x) = [x - 4] / [ (x +4)(x+9) ]
Find the limits when x approachs to each root.
Limit of f(x) when x approachs to - 4 by the right is negative infinite and limit when x approach - 4 by the left is infinite, then x = - 4 is a vertical asymptote.
Limit of f(x) when x approachs to - 9 by the left is negative infinite and limit when x approach - 9 by the right is infinite, then x = - 9 is a vertical asymptote.
Answer: x = -9 and x = -4 are the two asymptotes.
Answer:
D
Step-by-step explanation:
a is false since x could be 0.
b is easy to check, just plug numbers in, and we can see that it's false(you would get 0+0=1 and -0-0=-1 once plugged in)
c is also easy to check, just plot the line or simplify the first equation. since (2x+2y)/2=4/2 is also x+y=2, the second equation is also x+y=2, so it must have infinitely many solutions.
d must be true due to process of elimination but let's check to make sure.
7y=14x, divide both sides by 7 to get y=2x and since they're the same equation it must mean that they have infinitly many solutions and we can see that it is correct
Answer:
pretty sure its d
Step-by-step explanation:
the quadrant one function has asymptotes at y=0 and x=0 so x and y have to stay positive
the quadrant three function has asymptotes at y=0 and x=0 so x and y have to stay negative