Question
Look at the table of values for the functions f(x) and g(x).
x f(x)=2x g(x)=3x+25
0 1 25
1 2 28
2 4 31
3 8 34
4 16 37
5 32 40
Now, complete the sentence about the two functions.
As the value of x increases, the value of f(x) will
the value of g(x) because f(x) grows
and g(x) grows
x f(x)=2x g(x)=3x+25
0 1 25
1 2 28
2 4 31
3 8 34
4 16 37
5 32 40
Now, complete the sentence about the two functions.
As the value of x increases, the value of f(x) will
the value of g(x) because f(x) grows
and g(x) grows
Answers
GPT-4o mini
As the value of x increases, the value of f(x) will **become smaller than** the value of g(x) because f(x) grows **exponentially** and g(x) grows **linearly**.
To clarify:
- \( f(x) = 2^x \) is an exponential function.
- \( g(x) = 3x + 25 \) is a linear function.
As x increases, the rate of growth of \( f(x) \) becomes significant as it is based on powers of 2, while \( g(x) \) increases at a constant rate. However, from the values provided in the table, \( g(x) \) always remains greater than \( f(x) \) for the given x values.
To clarify:
- \( f(x) = 2^x \) is an exponential function.
- \( g(x) = 3x + 25 \) is a linear function.
As x increases, the rate of growth of \( f(x) \) becomes significant as it is based on powers of 2, while \( g(x) \) increases at a constant rate. However, from the values provided in the table, \( g(x) \) always remains greater than \( f(x) \) for the given x values.