1. Ch. 9.2 Graphing Inverse Variations

2. 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 – – –
y –0.05 –0.1 –0.25 –1 –2 – 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

3. 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

4. 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.

5. Check understanding
p. 486 # 2

6. 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

7. 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.

8. Graphing Inverse Variations
ALGEBRA 2 LESSON 9-2
Sketch the graph of y = 1
x + 2
Step 1: Draw the asymptotes.
For y = , 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

9. Check understanding
p. 487 # 5

10. 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
= Substitute 8 for b and 4 for c.
– 7
x – 8
= – 4 Simplify.
– 7
x – 8
9-2

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