Ch. 9.2 Graphing Inverse Variations

ALGEBRA 2 LESSON 9-2ALGEBRA 2 LESSON 9-2

Graphing Inverse VariationsGraphing Inverse Variations

Draw a graph of y = .0.5x

Make a table of values that includes positive and negative values of x. Notice that x cannot be 0.

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.

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

12

14

1 10

1 10

14

12

Connect them with a smooth curve.

9-2

ALGEBRA 2 LESSON 9-2ALGEBRA 2 LESSON 9-2

Graphing Inverse VariationsGraphing Inverse Variations

Compare the graphs of y = and y = shown below.0.25

x1x

The axes are the asymptotes for both graphs.

Both graphs are symmetric with respect to y = x and y = –x.

What points on the graphs are closest to the origin?

The points, (1, 1), (–1, –1), (0.5, 0.5), and (–0.5, –0.5) are closest to the origin.

The branches of y = are closer to the axis than are the branches of .0.25x

1x

9-2

EX. 2 ContinuedEX. 2 Continued

The intersections of the graphs with y = kx are :

The points, (1, 1), (–1, –1), (0.5, 0.5), and (–0.5, –0.5) are closest to the origin.

, ,k k and k k

where k is the constant of variation.

Check understandingCheck understanding

p. 486 # 2

ALGEBRA 2 LESSON 9-2ALGEBRA 2 LESSON 9-2

Graphing Inverse VariationsGraphing Inverse Variations

Compare the graphs of y = and y = – shown below.2x

2x

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 VariationTranslation of Inverse Variation

The graph of is a translation of

by b units horizontally and c units vertically.

ky c

x b

The vertical asymptote is x = b.

The horizontal asymptote is y = c.

ky

x

ALGEBRA 2 LESSON 9-2ALGEBRA 2 LESSON 9-2

Graphing Inverse VariationsGraphing Inverse Variations

Sketch the graph of y = + 2. 1 x + 2

Translate these points 2 units to the left and 2 units up to (–1, 3) and (–3, 1). Draw the branches through these points.

Step 2: Translate y = .

The graph y = includes (1, 1) and (–1, –1).

1x

1x

9-2

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

Check understandingCheck understanding

p. 487 # 5

ALGEBRA 2 LESSON 9-2ALGEBRA 2 LESSON 9-2

Graphing Inverse VariationsGraphing Inverse Variations

Write an equation for the translation of y = – that has

asymptotes at x = 8 and y = –4.

7x

9-2

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

HomeworkHomework

Page 488, Exercises: 1 – 3, 14 – 24 e