Question

A plecewise function is defined by f(x) = 3x + 1if < 1 and f (x) = -3x + 71f 2 > 1. Write the function as an absolute value function.

The absolute value function is f (x) =

Answer 1

To write the given piecewise function as an absolute value function, we can rewrite it using the switch condition. The absolute value function is f(x) = |3x + 1| - 70 when x < 1, and f(x) = -6x - 1 when x ≥ 1.

Step-by-step explanation:

To write the piecewise function as an absolute value function, we need to find the conditions where the two different expressions are defined. In this case, the function is defined as f(x) = 3x + 1 when x < 1, and f(x) = -3x + 71 when x ≥ 1. Notice that the switch happens at x = 1. We can rewrite the function as f(x) = |3x + 1| - (-3x + 71) when x < 1, and f(x) = -3x + 71 - (3x + 1) when x ≥ 1. Simplifying, we get f(x) = |3x + 1| + 3x - 3x + 1 - 71 = |3x + 1| - 70 when x < 1, and f(x) = -3x + 71 - 3x - 1 - 71 = -6x - 1 when x ≥ 1. So, the absolute value function is f(x) = |3x + 1| - 70 when x < 1, and f(x) = -6x - 1 when x ≥ 1.