Question

Given f(x) = x and h(x) = f(x) - 3, how does h(x) compare to f(x)?

a) h(x) is 3 units below f(x)
b) h(x) is 3 units above f(x)
c) h(x) is equal to f(x)

Answer 1

h(x) is derived by subtracting 3 from f(x), meaning it is 3 units below f(x) for any value of x.

Step-by-step explanation:

The function h(x) is defined in terms of f(x), where f(x) = x. Knowing that h(x) = f(x) - 3, we can deduce that for any given value of x, h(x) is going to be 3 units less than f(x). This is because the operation "- 3" subtracts 3 from the original value given by f(x). Therefore, for every x, h(x) lies 3 units below f(x) on a graph. So, the correct answer is h(x) is 3 units below f(x).