Model Inverse Variation Section 12.1

Objectives: Identify direct and inverse variation Graph inverse and direct variation equations Write inverse variation equations

Key Vocabulary: Inverse variation Constant of variation Hyperbola Branches of a hyperbola Asymptotes of a hyperbola

Inverse variation and Constant of variation Recall the two variables x and y show direct variation if y=ax. The variables x and y show inverse variation if y=a/x where a is nonzero. The nonzero number z is called the constant of variation.

Example 1: Tell whether the equation represents direct variation, inverse variation, or neither. .

#1: Tell whether the equation represents direct variation, inverse variation, or neither.

#2: Tell whether the equation represents direct variation, inverse variation, or neither.

#3: Tell whether the equation represents direct variation, inverse variation, or neither.

#4: Tell whether the equation represents direct variation, inverse variation, or neither.

Example 2: Graph the function.

Example 3: Graph the function.

Graphs

Hyperbolas, branches of hyperbolas, and asymptotes of hyperbolas The graph of an inverse variation equation is a hyperbola. The two symmetrical parts of a hyperbola are called the branches of the hyperbola. The lines that the hyperbola approaches but doesn’t intersect are called the asymptotes of the hyperbola. The asymptotes of an inverse variation equation are the x-axis and the y-axis.

Example 4: The variables x and y vary inversely, and y=6 when x=-3. Write an inverse variation equation that relates x and y. Find the vale of y when x=4.

#5: Graph the functions.

#6: Complete. The variables x and y vary inversely and y=-2 when x=12. Write an inverse variation equation that relates x and y. Then find the value of y when x=-3.

Example 5: Tell whether the table represents inverse variation. If so, write the inverse variation equation. x -5 -3 4 8 24 y 2.4 -1.5 -0.5

Example 6: A theater company plans to hire people to build a stage set. The work time t (in hours per person) varies inversely with the number p of people hired. The company estimates that 25 people working for 300 hours each can complete the job. Find the work time per person if the company hires 30 people.

#7: Tell whether the ordered pairs represent inverse variation #7: Tell whether the ordered pairs represent inverse variation. If so, write the inverse variation equation. (-5, 2), (-4, 2.5), (8, -1.25), (20, -0.5)

Homework Assignment Page 768 #6, 8, 10, 12, 14, 16, 18, 22, 24, 28, 30, 36, 38, 40, 42, 44, 46, 54