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Natali [406]
3 years ago
10

How would you describe the relationship between the real zeros and x-intercepts of the function y=log4(x-2)

Mathematics
2 answers:
notsponge [240]3 years ago
5 0

Answer:

Step-by-step explanation:

First, look at y = log x.  The domain is (0, infinity).  The graph never touches the vertical axis, but is always to the right of it.  A real zero occurs at x = 1, as log 1 = 0 => (1, 0).  This point is also the x-intercept of y = log x.

Then look at y = log to the base 4 of x.  The domain is (0, infinity).  The graph never touches the vertical axis, but is always to the right of it.  Again, a real zero occurs at x = 1, as log to the base 4 of 1 = 0 => (1, 0).

Finally, look at y=log to the base 4 of (x-2).  The graph is the same as that of y = log to the base 4 of x, EXCEPT that the whole graph is translated 2 units to the right.  Thus, the graph crosses the x-axis at (3, 0), which is also the x-intercept.

Nady [450]3 years ago
4 0

B. Since the graph never crosses the x-axis, the function has no real zeros.

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