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Stitz-Zeager_College_Algebra_e-book

# From the graph we determine the domain of h is and the

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Unformatted text preview: b, a) is perpendicular to the line y = x. Note: Coupled with the result from Example 1.1.6 on page 9, we have now shown that the line y = x is a perpendicular bisector of the line segment connecting (a, b) and (b, a). This means the points (a, b) and (b, a) are symmetric about the line y = x. (Can you see why?) We will revisit this symmetry in section 5.2. 15. The function deﬁned by I (x) = x is called the Identity Function. (a) Discuss with your classmates why this name makes sense. (b) Show that the point-slope form of a line (Equation 2.2) can be obtained from I using a sequence of the transformations deﬁned in Section 1.8. 16. Compute the average rate of change of the given function over the speciﬁed interval. (a) f (x) = x3 , [−1, 2] 1 (b) f (x) = , [1, 5] x √ (c) f (x) = x, [0, 16] (d) f (x) = x2 , [−3, 3] x+4 (e) f (x) = , [5, 7] x−3 (f) f (x) = 3x2 + 2x − 7, [−4, 2] 17. Compute the average rate of change of the given function over the interval [x, x + h]. Here we assume [x, x + h] is in the domain of each function. (a) f (x) = x3 (b) f (x) = 1 x x+4 x−3 (d) f (x) = 3x2 + 2x − 7 (c) f (x) = 18. With the help of your c...
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