Ch. 9.2 Graphing Inverse Variations

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Presentation transcript:

Ch. 9.2 Graphing Inverse Variations

Graphing Inverse Variations ALGEBRA 2 LESSON 9-2 Draw a graph of y = . 0.5 x Make a table of values that includes positive and negative values of x. Notice that x cannot be 0. 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 1 2 4 10 Connect them with a smooth curve. Graph the points. 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. 9-2

Graphing Inverse Variations ALGEBRA 2 LESSON 9-2 Compare the graphs of y = and y = shown below. 0.25 x 1 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 branches of y = are closer to the axis than are the branches of . 0.25 x 1 The points, (1, 1), (–1, –1), (0.5, 0.5), and (–0.5, –0.5) are closest to the origin. 9-2

The intersections of the graphs with y = kx are : EX. 2 Continued The intersections of the graphs with y = kx are : where k is the constant of variation. The points, (1, 1), (–1, –1), (0.5, 0.5), and (–0.5, –0.5) are closest to the origin.

Check understanding p. 486 # 2

Graphing Inverse Variations ALGEBRA 2 LESSON 9-2 Compare the graphs of y = and y = – shown below. 2 x Both graphs are symmetric with respect to y = x and y = –x. Each is a 90° rotation of the other about the origin. 9-2

Translation of Inverse Variation The graph of is a translation of by b units horizontally and c units vertically. The vertical asymptote is x = b. The horizontal asymptote is y = c.

Graphing Inverse Variations ALGEBRA 2 LESSON 9-2 Sketch the graph of y = + 2. 1 x + 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 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. 9-2

Check understanding p. 487 # 5

Graphing Inverse Variations ALGEBRA 2 LESSON 9-2 Write an equation for the translation of y = – that has asymptotes at x = 8 and y = –4. 7 x y = + c Use the general form of a translation. – 7 x – b = + 4 Substitute 8 for b and 4 for c. – 7 x – 8 = – 4 Simplify. – 7 x – 8 9-2

Homework Page 488, Exercises: 1 – 3, 14 – 24 e