direct and inverse variation. direct variation two functions are said to vary directly if as the...

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Direct and Inverse Variation

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Page 1: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Direct and Inverse Variation

Page 2: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Direct Variation

• Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other does as well.

Page 3: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

How do you know if you have a direct variation?

• Y varies directly to x• Y is directly

proportional to x• Y = kx for some

constant kaxy

Page 4: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Inverse Variation• An inverse variation function is defined by the equation

xy = k.

Page 5: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Functions

A relationship in which every value of x has a unique value of y.

In other words:

one y for every x

One output for each input

One response for each influence

One effect for each cause

Page 6: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Height is a Function of Weight

f(weight) = heightSimilar to f(x) = mx + b, where f(x) is the function notation to represent y. The letter or part in the parenthesis is always the independent variable.

Weight is input (x) and Height is output (y)

Page 7: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Example

Gross pay is a function of the hours you work times your rate of pay. Your hourly rate of pay is $6.50 a hour. Write the function to represent this situation.

Answer is f(h) = 6.50h

Page 8: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Domain

All the possible values for the independent variable.

Range

All the possible values for the dependent variable.

Page 9: Direct and Inverse Variation. Direct Variation Two functions are said to vary directly if as the magnitude of one increases, the magnitude of the other

Make a table to represent some values for your gross pay from the previous example f(h) = 6.50h

What are the domain and range of the function listed in the table?

What are the practical domain and range? (Assume 40 hour week)

h f(h)

2 13.00

5 32.50

10 65.00

17 110.50

40 260.00

**Remember practical domain is the values of the independent variable that makes sense and the practical range is the values you get after applying the domain to the function.(real life scenarios) Answer:

Domain { 0 through 40}Range {0 through 260}

Answer:Domain {2, 5, 10, 17, 40}Range {13, 32.5, 65, 110.5, 260}