Vertical Asymptote at x = -3 and x=4
g
When a function has vertical asymptotes at x = a and x = b, it means that the function approaches infinity or negative infinity as it gets closer and closer to those x-values.
To understand this concept better, let’s consider an example function:
f(x) = (x-2)/(x^2-9)
To find the vertical asymptotes of this function, we need to find the values of x for which the denominator of the function becomes zero. This is because dividing by zero is undefined.
So, let’s set the denominator equal to zero and solve for x:
x^2 – 9 = 0
(x-3)(x+3) = 0
x = 3 or x = -3
Therefore, the function has a vertical asymptote at x = -3.
Similarly, we need to find the denominator of the function that becomes zero at x=4:
x^2 – 9 = 0
(x-3)(x+3) = 0
x = 3 or x = -3
Since x = 4 is not a solution to the denominator of the function, we don’t have a vertical asymptote at x = 4.
In conclusion, the function has a vertical asymptote at x = -3, but not at x = 4.
More Answers:
Understanding Vertical Asymptotes at x=5 in Rational Functions: A Guide.Understanding Vertical Asymptotes: Examples of Functions without Vertical Discontinuity
How to Handle a Hole and Other Discontinuities in a Function: Tips and Tricks