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 exponentially?
g(x), f(x), x
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
Question 13 options:
1) f(x) because it eventually exceeds g(x)
2) g(x) because it eventually exceeds f(x)
3) f(x) because it eventually intersects g(x)
4) g(x) because it will not intersect f(x)

Answer 1

Answer:

Option 2 - g(x) because it eventually exceeds f(x)

Step-by-step explanation:

Given :  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.        

x    f(x)    g(x)

1      3       3

2     6       9

3     11      27

4     18      81

5     27     243        

To find : Which function is most likely increasing exponentially?

Solution :

The values of x and f(x) satisfying a quadratic equation,

$f(x)=x^2+2$

So, f(x) is quadratic function.

The values of x and g(x) satisfying a exponential equation,

$g(x)=3^x$

So, g(x) is exponential function.

Now, considering the table

We have seen that at the value of g(x) is greater than value of f(x)

As 3=3 , 6<9 , 11<27 ,18<81, 27<243

So, g(x) is eventually exceeds f(x).

Therefore, Option 2 is correct.

Answer 2

It's easy to see that g(x) = $3^{x}$
The answer is 2. g(x) because it eventually exceeds f(x).