Question

Let f be the function defined by f(x) = |x - 2| for all x. Which of the following statements is true?

1) f is a linear function
2) f is a quadratic function
3) f is an exponential function
4) f is a piecewise function

Answer 1

The function f(x) = |x - 2| is a piecewise function.

Step-by-step explanation:

The function f(x) = |x - 2| represents an absolute value function. It is neither a linear function nor a quadratic function, as it does not have a degree of 1 or 2. Instead, it is a piecewise function, which means its expression changes depending on the value of x. In this case, it can be defined as:

f(x) = x - 2, if x - 2 ≥ 0

f(x) = -(x - 2), if x - 2 < 0

Therefore, the correct statement is: f is a piecewise function.