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]
(b) f (x) = , [1, 5]
(c) f (x) = x, [0, 16] (d) f (x) = x2 , [−3, 3]
(e) f (x) =
, [5, 7]
(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
(d) f (x) = 3x2 + 2x − 7
(c) f (x) = 18. With the help of your c...
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