Question

a. Plot the data for the functions f(x) and g(x) on a grid and connect the points. x-2-1012 f(x)1/91/3139 x-2-1012 g(x)-4-2024 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.

Answer 1

I am going to insert a table, please wait a moment

`\begin{gathered} x\text{ f(x) g(x)} \\ -2\text{ }(1)/(9)\text{ -4} \\ -1\text{ }(1)/(3)\text{ -2} \\ 0\text{ 1 0} \\ 1\text{ 3 2} \\ 2\text{ 9 4} \end{gathered}`

Now I am going to draw the graphs, please wait a moment

Notice that from the shape of the plots we can assure that f(x) is an exponential function (in fact it is 3^x) and g(x) is a linear function (2x).

Also from the plot we notice that if the tendency continues then the lines will never touch, meaning that the functions well never hae equal values. Then functions will never be equal because 3^x > 2x for all x real number.