Question

The functions f(x) and g(x) are shown below:

f(x) = 2^x
g(x) = 2x

Which statement best describes the graph of f(x) and g(x)?

A- The graph of f(x) will eventually exceed the graph of g(x).

B- The graph of g(x) will eventually exceed the graph of f(x).

C- The graphs will both have their y-intercept equal to 1.

D- The graphs will both have their y-intercept equal to 2.

Answer 1

Option A. is the correct option.

Explanation:

The two functions are
`f(x)=2^(x)` and g(x) = 2x

If we analyze these functions over the graph we find that function g(x) is an line which intersect
`y=2^(x)` over the two points that means f(x) is exceeding g(x).

In other words if we draw the graph for both the functions with the different values of x, f(x) will have the higher values as compared to g(x).

For x = 0 1 2 3 4

f(x) = 1 2 4 8 16

g(x) = 0 2 4 6 8

Option A is the correct option.