what is the vertical asymptote of f(x)=x^3+2/x+5?
To find the vertical asymptote of the function f(x) = (x^3 + 2) / (x + 5), we need to determine where the function approaches infinity or negative infinity as x approaches a certain value.
The vertical asymptote occurs when the denominator of the fraction approaches zero, causing the value of the function to increase or decrease indefinitely. In this case, we can find the vertical asymptote by setting the denominator equal to zero and solving for x.
So, let's set x + 5 = 0 and solve for x:
x + 5 = 0
x = -5
Hence, the vertical asymptote of the function f(x) = (x^3 + 2) / (x + 5) is x = -5.
To summarize:
1. Set the denominator equal to zero: x + 5 = 0
2. Solve for x: x = -5
3. The vertical asymptote of the function is x = -5.