Complete the table of values for f(x)=3x+1 and g(x)=x2+5.
x f(x) g(x)
0
1
2
3
Both f(x) and g(x) grow as x gets larger and larger. Which function eventually exceeds the other?
To fill in the table of values:
For f(x) = 3x + 1:
x f(x)
0 1
1 4
2 7
3 10
For g(x) = x^2 + 5:
x g(x)
0 5
1 6
2 9
3 14
Both f(x) and g(x) grow as x gets larger and larger.
As x gets larger and larger, the function g(x) = x^2 + 5 eventually exceeds f(x) = 3x + 1 since the growth rate of a quadratic function (x^2) is larger than the linear function (3x).