Question

Error Analysis: Describe and correct the error a student made in expressing the function. f(x) = 3|x| as a piecewise-defined function​

Answer 1

• The comparison symbols need to be reversed
• f(x) = {3x, x≥0; -3x, x<0}

Explanation:

The absolute value function is {x, x≥0; -x, x<0} That needs to be multiplied by 3 to get the f(x) in the given problem.

f(x) = 3|x| = 3{x, x≥0; -x, x<0}

f(x) = {3x, x≥0; -3x, x<0} . . . . correct function definition

Compared to the student's answer, the student has reversed the comparison symbols.