Answer:
By examining the table of ordered pairs, notice that the function f(x) is the cube of [tex]x[/tex]. Therefore, [tex]f(x)=x^3[/tex]
By examining the table of ordered pairs, notice that as [tex]x[/tex] increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore, [tex]g(x)=3^x[/tex]
From the table, both functions equal 27 when [tex]x=3[/tex], therefore, the point of intersection of the two functions is (3, 27).
As x increases past [tex]x=3[/tex], g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.
So the following statements are true:
- f(x) is a polynomial function
- g(x) is an exponential function
- The output values of g(x) will surpass those of f(x) as the input values continue to increase.
Please refer to the attached graph of both functions with plotted ordered pairs.
