Question

Given f(x) = 3x - 1, the piecewise functions are:

a) f(x) = 3x - 1 for all x
b) No piecewise functions coincide with f(x)
c) There is not enough information to determine the piecewise functions
d) f(x) = 3x - 1 for x ≤ 1; f(x) = 0 for x > 1

Answer 1

The provided function, f(x) = 3x - 1, is not a piecewise function if it is defined for all x, but it becomes a piecewise function under the condition specified in option (d), where it takes on different expressions for different intervals of x.

Step-by-step explanation:

The student is asking about piecewise functions and whether the given function f(x) = 3x - 1 falls into that category. A piecewise function is defined by different expressions based on different intervals of the input x. The options seem to refer to various piecewise function definitions. Since f(x) = 3x - 1 is given as the definition for all x in option (a), it is not a piecewise function because it does not have different expressions for different intervals. Option (d) defines a piecewise function because f(x) = 3x - 1 for x ≤ 1, and f(x) = 0 for x > 1, which means it has different expressions for different intervals of x.