Answer:
Domain: (0, ∞)
Range: (-∞, ∞)
As x --> ∞ f(x) ---> ∞
As x --> 0 f(x) ---> -∞
x-intercept: (1, 0)
Asymptote: x = 0
Step-by-step explanation:
To graph the function, let's fill the following table:
x y
1 f(1) = log₃(1) = 0
3 f(3) = log₃(3) = 1
9 f(9) = log₃(9) = 2
Therefore, the graph for the function is:
Then, the domain of the function is the set of values that the variable x can take. Since logarithm is only defined for positive values, the domain is: (0, ∞)
The range is the set of values that the variable y can take. Since y can take any value, the range is (-∞, ∞)
The function goes to ∞ when x is greater and the function goes to -∞ when x is 0, so:
As x --> ∞ f(x) ---> ∞
As x --> 0 f(x) ---> -∞
The x-intercept is the value where the graph crosses the x-axis. Since it crosses the x-axis at (1, 0), the x-intercept is (1, 0)
The asymptote is a line that is never touched by the graph. Since the graph is not defined by x =0, the asymptote is x = 0.
So, the answers are:
Domain: (0, ∞)
Range: (-∞, ∞)
As x --> ∞ f(x) ---> ∞
As x --> 0 f(x) ---> -∞
x-intercept: (1, 0)
Asymptote: x = 0