Question

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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

f(3) > g(3) > h(3)

f(6) > g(6) > h(6)

As x is increasing and all the functions behaving alike so

f(15) > g(15) > h(15)

Explanation:

To check the incrasing order substitute values of x, firstly put x=3

we get,

f(3) = 34 , g(3) = 25 , h(3) = 5

thus

f(3) > g(3) > h(3)

Similarly,

f(6) = 91 , g(6) = 49 , h(6) = 14

f(6) > g(6) > h(6)

As x is increasing and all the functions behaving alike so

f(15) > g(15) > h(15)