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

2-108.
  1. Given: Homework Help ✎

    1. Rewrite h(x) as a piecewise function.

    2. Using set notation, state the domain and range of h(x).

    3. Estimate A(h, −1 ≤ x ≤ 3) by any method.

    4. 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 = |x² − 1| graph differs from y = x² − 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 = x² − 1.

x² − 1, x < −1
y = −x² + 1, −1 ≤ x ≤ 1
x² − 1, x > 1

Consider how the range of h(x) differs from the range of y = x² − 1.

A trapezoidal sum is an option.

The height is determined by the function.

Use the eTool below to help answer each part:
Click on the link to the right to view the full version of the eTool. Calc 2-108 HW eTool