MATH SOLVE

4 months ago

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

Accepted Solution

A:

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.