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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.

Sagot :

MrRoyalidn

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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