Exercise 31 Page 424

Practice makes perfect

a We will use the leftmost and the rightmost points to find the domain.

We see that the leftmost point on the graph is (- 4,3.2), and the rightmost point is (4,3.2). The x-coordinates of these points determine the domain. Domain: - 4 ≤ x ≤ 4 The domain of the function represents the width of the mouth of the glass, so it is 8 centimeters. 4-( - 4)=8

b When the rotational speed of the water increases, the parabolic cross section deepens. Therefore, our friend's claim is incorrect. If we model the parabolic cross section by y=0.1x^2, it would have a depth of 1.6 centimeters.

Slower rotational speed can create a cross section modeled by the function y=0.1x^2

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Exercise 31 Page 424

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