Question

3. Consider the functions f(x) = x2 + 10x – 5, g(x) = 8x + 1, and h(x) = 3x – 4. List the functions from least to greatest value when x = 3 and when x = 6. Then tell how you would explain to someone that you do not need to do any calculations to know the order of the functions when x = 15.

Answer 1

When x = 3:

f(3) = 3^2 + 10 (3) – 5 = 34

g(3) = 8 (3) + 1 = 25

h(3) = 3 (3) – 4 = 5

Therefore the order from least to greatest is: h(x), g(x), f(x)

When x = 6:

f(6) = 6^2 + 10 (6) – 5 = 91

g(6) = 8 (6) + 1 = 49

h(6) = 3 (6) – 4 = 14

Therefore the order from least to greatest is: h(x), g(x), f(x)

We don’t need to do any calculations to know the order when x = 15 since all the values are increasing and it is shown that the order would remain the same.