Question

The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically?

x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243

Answer 1

f(x), because it grows faster than g(x)
g(x), because it will not intersect f(x)
g(x), because it grows slower than f(x)
f(x), because it grows slower than g(x)

Answer 2

F(x) = AX^n+BX+C = quadratic
Exponential f(x) = n^x

Answer 3

They intersect at the point (1,3) so that choice that says that is wrong

Answer 4

I would say F(x) because it grows slower than g(x) that's how we know f(x) is quadratic.

Answer 5

Phantom336 is correct. Something that really stuck out in this problem is the way that these functions would be graphed.

Look at g(x).
When x=1 y=3
When x=2 y=9
When x=3 y=27
When x=4 y=81
When x=5 y=243

Notice that y is increasing exponentially (which kind of gives away that g(x) is the exponential function. \[3^{1}=3; 3^{2}=9; 3^{3}=27; 3^{4}=81; 3^{5}=243\]

Also notice that the graph would curve upwards which is an indicator of an exponential function:



So there are a few quick tricks to use when you see this kind of problem again in the future. Hope it helps!