Question

Which piecewise function coincides with f(x)=|−x−3|2−1?

Answer 1

f(x)=−(x+3)2−1 when x < 3

f(x)=−(x+3)2−1 when x ≤ -3

f(x)=−(x−3)2−1 when x ≥ 3

f(x)=(x+3)2−1 when x < -3

Answer 2

@iGreen

Answer 3

\[|-x-3|^2-1~~=~~\left(|-1||x+3|\right)^2-1~~=~~|x+3|^2-1\]
Consider the graph of \(y=(x+3)^2\):

Since every value of \(y\) is positive, you know that \(|x+3|^2=(x+3)^2\).

So what this means is
\[|-x-3|^2-1=(x+3)^2-1\]
If you know the plot of one, you know the plot of the other.

Answer 4

In terms of a piecewise function, only the last option agrees with the above.