Complete the table of values for f(x)=4x–1 and g(x)=2x2+2.
x f(x) g(x)
2
3
4
5
Both f(x) and g(x) grow as x gets larger and larger. Which function eventually exceeds the other?
To find the values of f(x) and g(x) for the given x values, we can plug each x value into the respective functions.
For f(x) = 4x - 1:
x f(x)
2 4(2) - 1 = 7
3 4(3) - 1 = 11
4 4(4) - 1 = 15
5 4(5) - 1 = 19
For g(x) = 2x^2 + 2:
x g(x)
2 2(2)^2 + 2 = 10
3 2(3)^2 + 2 = 20
4 2(4)^2 + 2 = 34
5 2(5)^2 + 2 = 52
As x gets larger and larger, g(x) exceeds f(x) because the leading term in g(x) (2x^2) grows faster than the leading term in f(x) (4x).