Graph D will represent the given piecewise function.
Piecewise function:
- Piecewise function is defined by the pieces of curves or lines over the different intervals.
Given in the question,
- Equation of the piecewise function,
f(x) = (x + 2)² If x < -1
|x - 1| If -1 ≤ x ≤ 1
[tex]-\sqrt[3]{x}[/tex] If x > 1
For the given interval (x < -1),
Since, f(x) = (x + 2)² is a quadratic function, it will be shown by a parabola starting with a hollow circle.
Present in each graph.
For the interval (-1 ≤ x ≤ 1),
In this interval the given function is,
f(x) = |x - 1|
And the function will be a straight line having points as,
x -1 0 1 2
y 2 1 0 1
Present in each graph.
For the interval (x > 1),
Given function is,
f(x) = [tex]-\sqrt[3]{x}[/tex]
Points lying on the graph,
x 2 3 4 5 6
y -1.26 -1.44 -1.59 -1.71 -1.82
These points are present in graph D.
Therefore, Graph D will be the answer.
Learn more about the piecewise functions here,
https://brainly.com/question/17966003?referrer=searchResults
