### Home > CALC > Chapter 2 > Lesson 2.3.1 > Problem 2-108

Given:

Homework Help ✎ Rewrite

*h*(*x*) as a piecewise function.Using set notation, state the domain and range of

*h*(*x*).Estimate

*A*(*h*, −1 ≤*x*≤ 3) by any method.Write a Riemann sum to approximate

*A*(*h*, −1 ≤*x*≤ 3) with 24 rectangles of equal width and evaluate the sum.

Notice how this *y* = |*x*² − 1| graph differs from *y* = *x*² − 1. From this we can determine that there will be three pieces, and we already know the first and last piece.

The middle piece is a vertical reflection of *y* = *x*² − 1.

*x*² − 1, *x* < −1*y* = −*x*² + 1, −1 ≤ *x* ≤ 1 *x*² − 1, *x* > 1

Consider how the range of *h*(*x*) differs from the range of *y* = *x*² − 1.

A trapezoidal sum is an option.

The height is determined by the function.

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