Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: xist. |x + 4 | x+4 |2 − x| (g) f (x) = 2−x 1 (h) f (x) = |2x − 1| 3 (i) f (x) = |x + 4| + |x − 2| (a) f (x) = |x + 4| (f) f (x) = (b) f (x) = |x| + 4 (c) f (x) = |4x| (d) f (x) = −3|x| (e) f (x) = 3|x + 4| − 4 2. With the help of your classmates, prove the second, third and ﬁfth properties listed in Theorem 2.1. 3. With the help of your classmates, ﬁnd a function involving absolute values whose graph is given below. y 4 3 2 1 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 x 4. With the help of your classmates, prove the following two properties of absolute value. (a) (The Triangle Inequality) For all real numbers a and b, |a + b| ≤ |a| + |b|. (b) If |f (x)| = |g (x)| then either f (x) = g (x) or f (x) = −g (x). 5. Use the result from Exercise 4b above to solve the following equations. Interpret your results graphically. (a) |3x − 2| = |2x + 7| (b) |3x + 1| = |4x| (c) |1 − 2x| = |x + 1| (d) |2 − 5x| = 5|x + 1| 136 2.2.2 Linear and Quadratic Functions Answers 1. (a) f (x) = |x + 4| f (−4) = 0 x-intercept (−4, 0) y -intercept (...
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