To find the equation of the vertical asymptote for the function [tex]\( f(x) = \log(x + 2) \)[/tex], follow these steps:
1. Identify the argument of the logarithmic function: The argument inside the logarithm function is [tex]\( x + 2 \)[/tex].
2. Determine where the argument is zero: A vertical asymptote for a logarithmic function occurs where the argument of the logarithm is zero because the logarithm of zero is undefined. Set up the equation to find where the argument is zero:
[tex]\[
x + 2 = 0
\][/tex]
3. Solve for [tex]\( x \)[/tex]: Solve the equation [tex]\( x + 2 = 0 \)[/tex]:
[tex]\[
x + 2 = 0 \\
x = -2
\][/tex]
4. Write the equation of the vertical asymptote: Since the function [tex]\( f(x) = \log(x + 2) \)[/tex] is undefined when [tex]\( x = -2 \)[/tex], the vertical asymptote is a vertical line where [tex]\( x = -2 \)[/tex]. Therefore, the equation of the vertical asymptote is:
[tex]\[
x = -2
\][/tex]
Thus, the vertical asymptote of the function [tex]\( f(x) = \log(x + 2) \)[/tex] is given by the equation [tex]\( x = -2 \)[/tex].
