Question

4. Here are the equations that define three functions.

Answer 1

The functions f(x), g(x) and h(x) are all linear functions

• The function value that is largest is h(-100)
• The function value that is largest is h(-100)
• The function value that is largest is f(1/100)

How to determine the function with the largest values

The functions are given as:

$f(x) = 4x - 5$

$g(x) = 4(x - 5)$

$h(x) = x/4 -5$

At x = 100, we have:

$f(100) = 4 * 100 - 5 = 395$

$g(100) = 4 * (100 - 5) = 380$

$h(100) = 100/4 - 5 = 20$

Hence, the function value that is largest is f(100)

At x = -100, we have:

$f(-100) = -4 * 100 - 5 = -405$

$g(-100) = 4 * (-100 - 5) = -420$

$h(-100) = -100/4 - 5 = -30$

Hence, the function value that is largest is h(-100)

At x = 1/100, we have:

$f(1/100) = 4/100 - 5 = -4.96$

$g(1/100) = 4 * (1/100 - 5) = -19.96$

$h(1/100) = (1/100)/4 - 5 = -4.9975$

Hence, the function value that is largest is f(1/100)

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