Question

Which statement about the end behavior of the logarithmic function f(x) = log(x+3)-2 is true?

A. As x decreases to the vertical asymptote at x = -3, y decreases to negative infinity.
B. As x decreases to the vertical asymptote at x = -1, y decreases to negative infinity.
C. As x decreases to the vertical asymptote at x = -3, y increases to positive infinity.
D. As x decreases to the vertical asymptote at x = -1, y increases to positive infinity.

Answer 1

A

Explanation:

As you should know, in a log function f(x) = a * log[k(x-d)] + c, the variable d would be your asymptote. Since the a value of the function is 1, nothing has been done to the graph and thus we can assume that it goes in the same direction of the parent function f(x) = log x. Therefore, as the x value gets closer to -3, the y value will continue to negative infinity.