Question

3. Describe and correct the error a student made in determining the relationship between the domain and range of f(x) = 10[x] and f(x)= |x|.

The domain of f(x) = 10|x| is the same as the domain of f(x) = 10[x]. The range of f(x) = 10|x| is 10 times the range of f(x) =[x]​

Answer 1

The student's error is in describing the range

The range of f(x) = 10|x| is f(x) ≥ 0

The range of f(x) = 10{x] is all real number

How to find the error

Absolute value functions are always positive and hence does not include negative numbers in their output.

This makes range of absolute value function to be f(x) ≥ 0

For the linear function, f(x) = 10x, the output includes negative numbers. Hence the range for f(x) = 10x is all real numbers