Complete the table of values for f(x)=2x2+1 and g(x)=5x+5.
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) at each x, we can plug in the given x values into the respective functions:
f(x) = 2x^2 + 1
g(x) = 5x + 5
Plugging in x = 2:
f(2) = 2(2)^2 + 1 = 2(4) + 1 = 8 + 1 = 9
g(2) = 5(2) + 5 = 10 + 5 = 15
Plugging in x = 3:
f(3) = 2(3)^2 + 1 = 2(9) + 1 = 18 + 1 = 19
g(3) = 5(3) + 5 = 15 + 5 = 20
Plugging in x = 4:
f(4) = 2(4)^2 + 1 = 2(16) + 1 = 32 + 1 = 33
g(4) = 5(4) + 5 = 20 + 5 = 25
Plugging in x = 5:
f(5) = 2(5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51
g(5) = 5(5) + 5 = 25 + 5 = 30
Comparing the values of f(x) and g(x) for each given x, we see that for x = 2, g(x) exceeds f(x). For x = 3, 4, and 5, f(x) exceeds g(x). Therefore, f(x) eventually exceeds g(x) for x greater than or equal to 3.