Questions: Consider the function f(x)=log6(x) a. Graph the function. b. Equation of the asymptote: c. Domain in interval notation: d. Range in interval notation:

Solution Steps

The given function is \( f(x) = \log_6(x) \). This is a logarithmic function with base 6. Logarithmic functions have a vertical asymptote at \( x = 0 \) and pass through the point \( (1, 0) \).

To graph \( f(x) = \log_6(x) \):

1. Identify the vertical asymptote at \( x = 0 \).
2. Plot key points such as \( (1, 0) \) and \( (6, 1) \) because \( \log_6(1) = 0 \) and \( \log_6(6) = 1 \).
3. Draw the curve passing through these points, approaching the vertical asymptote as \( x \) approaches 0 from the right.

The vertical asymptote of the function \( f(x) = \log_6(x) \) is at \( x = 0 \).

Final Answer