Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.)
f(x) = 3/(x – 6)^3
Well, well, well, let's figure out those vertical asymptotes, shall we?
To find the vertical asymptotes, we look for values of x that make the denominator equal to zero. In this case, the denominator is (x - 6) cubed. If we set it equal to zero and solve for x, we get x = 6.
So, my friend, the vertical asymptote of your function f(x) = 3/(x - 6)^3 is x = 6. It's like a barrier, preventing our graph from reaching that forbidden territory.
To find the vertical asymptotes of the function f(x) = 3/(x – 6)^3, we need to determine the values of x where the function approaches positive or negative infinity.
Vertical asymptotes occur when the denominator of a fraction approaches zero while the numerator remains non-zero.
In this case, we have a vertical asymptote when (x – 6)^3 = 0.
To find the value of x that makes the denominator zero, we solve the equation:
(x – 6)^3 = 0
Taking the cube root of both sides, we get:
x – 6 = 0
Adding 6 to both sides, we find:
x = 6
Thus, the vertical asymptote of f(x) = 3/(x – 6)^3 is x = 6.
To find the vertical asymptotes of a function, you need to determine the values of x for which the function approaches infinity or negative infinity.
In this case, the given function is f(x) = 3/(x – 6)^3.
To find the vertical asymptotes, we need to identify any values of x that would make the denominator equal to zero. These values would result in division by zero, which is undefined.
So, we set the denominator (x – 6)^3 equal to zero: (x – 6)^3 = 0.
To solve this equation, we take the cube root of both sides: x – 6 = 0.
Solving for x, we find x = 6.
Therefore, the vertical asymptote of the graph of f(x) = 3/(x – 6)^3 is x = 6.
Alternatively, you can also find the vertical asymptote by looking at the degree of the denominator. Since (x – 6)^3 is raised to the power of 3, the degree of the denominator is 3. Therefore, the vertical asymptote is given by the value where the denominator equals zero, which is x = 6.
Vertical asymptotes are caused by divisions by zero
so x-6 ≠ 0
x ≠ 6
then the VA is x = 6