Question

The graph of f(x) = 10 - ln(6x - 12) has a vertical asymptote at x = Option 1: x = 0 Option 2: x = 12/6 Option 3: x = 2 Option 4: x = 1

Answer 1

The graph of f(x) = 10 - ln(6x - 12) has a vertical asymptote at x = 2.

Step-by-step explanation:

The graph of f(x) = 10 - ln(6x - 12) has a vertical asymptote at x = 2.

To find the vertical asymptote, we need to find the value of x that makes the denominator of the natural logarithm equal to zero. In this case, the denominator is 6x - 12. So, we set 6x - 12 = 0 and solve for x.

6x = 12
x = 2

Therefore, the graph of f(x) has a vertical asymptote at x = 2.

Answer 2

The vertical asymptote for the function f(x) = 10 - ln(6x - 12) is at x = 2, corresponding to Option 3.

The correct option is option 3.

Step-by-step explanation:

To find the vertical asymptote of the function f(x) = 10 - ln(6x - 12), we need to determine the value of x at which the function approaches infinity. In the given function, the logarithmic part becomes undefined when its argument, 6x - 12, is equal to zero. Thus:

6x - 12 = 0

6x = 12

x = 2

Hence, the vertical asymptote occurs at x = 2, which corresponds to Option 3: x = 2.

The correct option is option 3.