A. plot the data for the functions f(x) and g(x) on a grid and connect the points.
x -2 -1 0 1 2 x -2 -1 0 1 2
f(x) 1/9 1/3 1 3 9 g(x) -4 -2 0 2 4
b. which function could be described as exponential and which as linear? explain.
c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.

  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.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!