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Section 9.2

Section 9.2. The Reciprocal Function Family. The Reciprocal Function Family. ALGEBRA 2 LESSON 9-2. (For help, go to Lesson 2-6.). Each of the following equations is a translation of y = | x |. Describe each translation. 1. y = | x | + 2 2. y = | x + 2|

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Section 9.2

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  1. Section 9.2 The Reciprocal Function Family

  2. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 (For help, go to Lesson 2-6.) Each of the following equations is a translation of y = |x|. Describe each translation. 1.y = |x| + 2 2.y = |x + 2| 3.y = |x| – 3 4.y = |x – 3| 5.y = |x + 4| – 5 6.y = |x – 10| + 7 Check Skills You’ll Need 9-2

  3. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 Solutions 1.y = |x| + 2 is y = |x| translated 2 units up. 2.y = |x + 2| is y = |x| translated 2 units left. 3.y = |x| – 3 is y = |x| translated 3 units down. 4.y = |x – 3| is y = |x| translated 3 units right. 5.y = |x + 4| – 5 is y = |x| translated 4 units left and 5 units down. 6.y = |x – 10| + 7 is y = |x| translated 10 units right and 7 units up. 9-2

  4. 0.5 x Draw a graph of y = . Make a table of values that includes positive and negative values of x. Notice that x cannot be 0. 1 4 1 10 1 10 1 4 1 2 1 2 x –10 –5 –2 – – – 2 5 10 y –0.05 –0.1 –0.25 –1 –2 –5 5 2 1 0.25 0.1 0.05 Graph the points. Connect them with a smooth curve. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 The graph has two parts. Each part is called a branch. The x-axis is the horizontal asymptote. The y-axis is the vertical asymptote. Quick Check 9-2

  5. 1 x 0.25 x Compare the graphs of y = and y = shown below. 1 x 0.25 x The branches of y = are closer to the axis than are the branches of . The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 Quick Check What points on the graphs are closest to the origin? The axes are the asymptotes for both graphs. Both graphs are symmetric with respect to y = x and y = –x. The points, (1, 1), (–1, –1), (0.5, 0.5), and (–0.5, –0.5) are closest to the origin. 9-2

  6. 2 x 2 x Compare the graphs of y = and y = – shown below. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 Both graphs are symmetric with respect to y = x and y = –x. Each is a 90° rotation of the other about the origin. Quick Check 9-2

  7. The frequency f in hertz of a sound wave varies inversely with its wavelength w. The function f = models the relationship between f and w for a wave with a velocity of 343 m/s. Find the wavelength of a sound wave with a frequency of 440 Hz. 343 w Use the Intersection feature. 343 w Graph the functions f = and f = 440. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 Quick Check The wavelength is about 0.78 m/s. 9-2

  8. 1 x + 2 Sketch the graph of y = + 2. Step 1: Draw the asymptotes. For y = + 2, b = –2 and c = 2. The vertical asymptote is x = –2. The horizontal asymptote is y = 2. 1 x + 2 1 x Step 2: Translate y = . The graph y = includes (1, 1) and (–1, –1). 1 x Translate these points 2 units to the left and 2 units up to (–1, 3) and (–3, 1). Draw the branches through these points. The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 Quick Check 9-2

  9. 6 x 12 x 2. Compare the graphs of y = and y = . Answers may vary. Sample: both graphs lie in quadrants I and III. Both have the axes as asymptotes. Both are symmetric with respect to y = x and y = –x.The graph of y = can be obtained by stretching the graph of y = by a factor of 2. 12 x 6 x 3. A group of college students rents a large two-story house. The amount of rent in dollars that each student pays per month is inversely proportional to the number of students. The rent r per month for one student is related to the number of students n by the equation r = . Find the monthly rent each student pays if there are 8 students in the house. 1200 n 4. Sketch the asymptotes and the graph of y = – – . 0. 5 x + 2 1 2 13 x – 5 y = – 8 The Reciprocal Function Family ALGEBRA 2 LESSON 9-2 12 x 1. Draw a graph of y = . $150 5. Write an equation for the translation of y = that has asymptotes at x = 5 and y = –8. 13 x 9-2

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