Question

A. Plot the data for the functions f(x) and g(x) on a grid and connect the points.

Answer 1

Answer:

  a) see the plots below

  b) f(x) is exponential; g(x) is linear (see below for explanation)

  c) the function values are never equal

Step-by-step explanation:

a) a graph of the two function values is attached

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b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).

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c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.

In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.