Complete the table of values for f(x)=5x+4 and g(x)=x2+2x+3.
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 complete the table of values for f(x)=5x+4 and g(x)=x^2+2x+3, we plug in each x value into the respective functions:
For f(x)=5x+4:
x f(x)
2 14
3 19
4 24
5 29
For g(x)=x^2+2x+3:
x g(x)
2 11
3 14
4 19
5 26
Both f(x) and g(x) grow as x gets larger and larger. However, the function g(x) (x^2+2x+3) eventually exceeds f(x) (5x+4) as x gets larger. This is because as x increases, the quadratic function g(x) grows faster than the linear function f(x).