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

x = 3
f(x) = x²+ 10x - 5
f(3) = (3)² + 10(3) - 5
f(3) = 9 + 30 - 5
f(3) = 39 - 5
f(3) = 34

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

h(x) = 3x - 4
h(3) = 3(3) - 4
h(3) = 9 - 4
h(3) = 5

x = 6
f(x) = x² + 10x - 5
f(6) = (6)² + 10(6) - 5
f(6) = 36 + 60 - 5
f(6) = 96 - 5
f(6) = 91

g(x) = 8x + 1
g(6) = 8(6) + 1
g(6) = 48 + 1
g(6) = 49

h(x) = 3x - 4
h(6) = 3(6) - 4
h(6) = 18 - 4
h(6) = 14

I would explain to someone that you don't need to do any calculations to know the order of the functions when x is equal to 15 by knowing that f(x) is equal to 370, g(x) is equal to 121, and h(x) is equal to 41 to know that it is easy finding the function of x without calculating the answer.