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Lerok [7]
3 years ago
12

MARKIN BRAINIEST!!! PLZ HELP!!!

Mathematics
1 answer:
ira [324]3 years ago
8 0

Answer:

  • (4, 5)
  • remain constant and increase
  • g(x) exceeds the value of f(x)
  • eventually

Step-by-step explanation:

a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).

__

b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).

__

c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:

  f(8) = 4·8 +3 = 35

  g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35

  g(8) > f(8)

__

d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).

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