Question

A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?

graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37

f(x), because an increasing quadratic function will eventually exceed an increasing exponential function
g(x), because an increasing exponential function will eventually exceed an increasing quadratic function
f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect
g(x), because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect

Answer 1

Explanation:

Given that g(x) has ordered pairs as (0,1) (1,2), (3,8) (5,32) and (6,64)

Hence this is exponential as

`y =2^x`

g(x) contains points as (0,1) (1,2) (3,10), (5,26) and (6,37)

This seems to be quadratic

`y = x^2+1`

g(x) and f(x) start same but g(x) increases initially faster and then decreases

Hence correct option is

g(x), because an increasing exponential function will eventually exceed an increasing quadratic function

Answer 2

The graph that most likely represents the exponential function is that "f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect."

g(x) has the ordered pairs 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64.
f(x) has the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37.

Both functions are increasing.