Answer:
The function Ƒ(x) = -5|x| is a piecewise-defined function that calculates the value of the absolute value of x, and then multiplies it by -5.
To understand how the function works, let's break it down into two cases:
1. When x is positive or zero:
In this case, the absolute value of x is the same as x itself, since x is already positive or zero. So, if x is positive or zero, the function Ƒ(x) = -5 * x.
For example, if x = 3, then the absolute value of 3 is 3. Multiplying it by -5 gives us -15. Therefore, Ƒ(3) = -15.
2. When x is negative:
In this case, the absolute value of x is the opposite of x. So, if x is negative, the absolute value of x becomes -x. Therefore, if x is negative, the function Ƒ(x) = -5 * (-x).
For example, if x = -2, then the absolute value of -2 is 2. Multiplying it by -5 gives us -10. Therefore, Ƒ(-2) = -10.
To summarize:
- For x ≥ 0 (positive or zero), Ƒ(x) = -5 * x.
- For x < 0 (negative), Ƒ(x) = -5 * (-x).
Remember that the absolute value of a number is always positive, so regardless of the value of x, the result of Ƒ(x) will always be negative or zero.