Question

Consider the function f(x)=−2∣x+1∣+3. Give the piecewise linear function that corresponds to the absolute value function. If x⩽ then f(x)= ____ and If x> then f(x)= _____.

Answer 1

The piecewise linear function that corresponds to the absolute value function f(x) = -2|x+1|+3 is f(x) = -2x+1 for x ≤ -1 and f(x) = -2x+1 for x > -1.

Step-by-step explanation:

The given function is f(x) = -2|x+1|+3. The piecewise linear function that corresponds to the absolute value function can be found by considering the sign of the expression inside the absolute value.

If x ≤ -1, then f(x) = -2(-x-1)+3 = -2x+1.

If x > -1, then f(x) = -2(x+1)+3 = -2x+1.