Question

Please help I don’t understand

Answer 1

This is a piecewise defined function. We usually work with function that have a unique definition: for example, $f(x) = 3x+2$ means that, no matter which x-value you choose as input, the ouput will always be three times the input plus two, i.e. $3x+2$.

Piecewise function, instead, change the formula depending on the input. A piecewise function work like this: it tells you "if you give me an input within this range, then the output will be like this, otherwise..."

For example, in your case, if you feed this function with an input which is smaller than -9, the output will be 4.

If the input will be greater than or equal to -9, but less than -4, the ouput will be -3

If the input will be greater than or equal to -4, but less than -2, the ouput will be 0

If the input will be greater than or equal to -2, but less than 1, the ouput will be -1

Finally, if the input is greater than or equal to 1, the output is 3.

So, when you want to evaluate the function at x=-4, we fall in the case "the input is greater than or equal to -4, but less than -2", and thus the ouput is 0.

Similarly, the case x=0 falls in the case "between -2 and 1", so the answer is -1