college algebra word problem

Question

State the vertical asymptote of the function.

g(x) = ln(2x + 14) − 18.

 

 

Answer 1

Let 2x+14 = 0, then x= -14/2 = -2. When x=-2, g(x) is undefined or approaches negative infinity. negative infinity -18 is still negative infinity. x=-2 is the vertical asymptote of g(x). There is no natural logarithm of 0, but as you approach 0 from the positive side, you get ever decreasing values of the logarithm. And the graph gets ever closer to the vertical line x=-2 for x values very near -2, as long as x is slightly greater than -2. If x is slightly smaller or < -2 there is no graph. Although Euler with his identity shows while there is no real solution, there may be imaginary solutions.