Question

Describe the features of the function f(x) = 2log3(x - 2). The function has an asymptote at ____. The range of the function is ____, and it is on its domain of ____. The end behavior on the left side is ____, and the end behavior on the right side is ____.

Answer 1

The function f(x) = 2log3(x - 2) has an asymptote at x = 2, a range of all real numbers, and a domain of x > 2. The end behavior on the left side is negative infinity, and the end behavior on the right side is positive infinity.

Step-by-step explanation:

The function f(x) = 2log3(x - 2) has several features:

• Asymptote: The function has a vertical asymptote at x = 2, since the logarithm of a negative number is undefined.
• Range: The range of the function is all real numbers, since the logarithm of any positive number is defined.
• Domain: The function is defined for x > 2, since the logarithm requires its argument to be positive.
• End Behavior on the Left Side: As x approaches 2 from the left side (x < 2), the function approaches negative infinity.
• End Behavior on the Right Side: As x approaches infinity (x > 2), the function also approaches infinity.