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 = |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