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.

Answers

  1. 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
    Add 4 to both sides
    x = 5
    Set the radical to 0, to determine the asymptote
    x – 4 = 0
    Add 4 to both sides
    x = 4
    Hence, the x-intercept and the asymptote of g(x) are x = 5 and x = 4, respectively
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