Question

The table 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)
2 9 9
3 15 27
4 23 81
5 33 243
Which function is most likely increasing quadratically?

a
g(x), because it will not intersect f(x)

b
g(x), because it grows slower than f(x)

c
f(x), because it grows faster than g(x)

d
f(x), because it grows slower than g(x)

Answer 1

To determine which function is most likely increasing quadratically, we can compare the differences in the values of f(x) and g(x) for increasing values of x.

Looking at the table, we can see that as x increases, the values of f(x) and g(x) also increase. However, the rate of increase for f(x) appears to be larger than the rate of increase for g(x).

For example, when x increases from 2 to 3, f(x) increases by 6 (from 9 to 15), while g(x) increases by 18 (from 9 to 27). Similarly, when x increases from 4 to 5, f(x) increases by 10 (from 23 to 33), while g(x) increases by 162 (from 81 to 243).

Based on these differences, it seems that f(x) is growing faster than g(x) as x increases. This suggests that f(x) is most likely increasing quadratically, while g(x) is increasing at a slower rate.

Therefore, the correct answer is:

c) f(x), because it grows faster than g(x)

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