Question

Question 11(Multiple Choice)
(05.06 MC)
Using the graph of the function g(x) = log3 (x-4), what are the x-intercept and asymptote of g(x)?

The x-intercept is 3, and the asymptote is located at x = 4.
The x-intercept is 5, and the asymptote is located at x = 4.
The x-intercept is 4, and the asymptote is located at y = 5.
The x-intercept is 5, and the asymptote is located at y = 3.

1. thongdat2
The x-intercept and the asymptote of g(x) are x = 5 and x = 4, respectively

### How to determine the x-intercept and asymptote of g(x)?

The equation of the function is given as:
g(x)  = log3 (x – 4)
Set the function to 0, to determine the x-intercept
log3 (x – 4) = 0
Express the function as an exponential function
x – 4 = 3^0
Evaluate the exponent
x – 4 = 1