Question

Select the correct answer from each drop-down menu. Conisider the function f(x)=|(-2-8)/(2)|-1 The piecewise functions that coincide with the given function are and Reset Next

Answer 1

The correct piecewise functions that coincide with the given function f(x) = |(-2-8)/(2)|-1 are f(x) = 4 for x < 0 and f(x) = 4 for 0 ≤ x < ∞, which graphically represent a horizontal line at y = 4.

Step-by-step explanation:

The question involves identifying the correct piecewise functions that define the given function f(x) = |(-2-8)/(2)|-1. First, simplify the function: f(x) = |(-10)/(2)|-1 = 5-1 which simplifies to f(x) = 4. This expresses a constant function, meaning for every input x, the output is the constant value 4.

As a piecewise function, this can be written as:

• For x < 0: f(x) = 4
• For 0 ≤ x < ∞: f(x) = 4

Graphically, this represents a horizontal line at y = 4, which is the same across all pieces of the domain.