Question

I wil Mark BRANLIEST!! HELP!!!! Consider the graphs of linear function f(x) = 3x, quadratic function g(x) = 3x2, and exponential function h(x) = 2x. Which statement about the functions f, g, and h is correct?
A. As x increases, the value of f(x) will eventually exceed the values of g(x) and h(x).
B. As x increases, the value of g(x) will eventually exceed the values of f(x) and h(x).
C. As x increases, the value of h(x) will eventually exceed the values of f(x) and g(x).
D. As x increases, the values of both f(x) and g(x) will eventually exceed the value of h(x).
Here the Graph: https://www.savvasrealize.com/community/proxy/assessment/68bd51a0599744be92849bd2e08be180/images/bdbcc6b2-8670-4ddc-95a2-a48b6d6da348

Answer 1

Answer:

Option C.

Step-by-step explanation:

We know that, for a value a > 1.

if b > c, then:

a^b > a^c

Now, this means that if we have two functions:

f(x) = x^n

g(x) = x^m

and m > n

then for large values of x, g(x) will be larger than f(x), because g(x) has a larger exponent.

now, is also true that:

f(x) = x^n

g(x) = n^x

for n > 1

For large values of x, g(x) will be larger than f(x), again, because for larger values of x g(x) will have a really large exponent, thus it grows really fast.

Then we can conclude that for the functions:

f(x) = 3*x

g(x) = 3*x^2

h(x) = 2^x

For a given value of x, h(x) will exceed the other two functions.

This can be seen in the graph below, where:

h(x) is purple, g(x) is blue, and f(x) is green.

We can see that eventually, h(x) exceeds the other two.

The correct option is C.