4. Polynomial and Rational Functions

Solve Combined Variation Problems

Modeling Using Variation

Joint and Combined Variation

Identify direct and inverse variation by looking at the shape of graphs

Combined Variation Word Problem

Direct Variation / Direct Proportion - Example 1

In Exercises 45–46, describe in words the variation shown by the given equation.

z = kx^2 √y

Pre-Calculus - Solving a direct variation problem

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies directly as x. y = 65 when x = 5. Find y when x = 12.

Direct Variation / Direct Proportion - Example 3

Word problem on inverse variation

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as z and the difference between y and w.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies directly as x and inversely as the square of z. y = 20 when x = 50 and z = 5. Find y when x = 3 and z = 6.

Solve the variation problems in Exercises 77–82. The distance that a body falls from rest is directly proportional to the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds?

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies directly as the cube of z and inversely as y.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies directly as z and inversely as the difference between y and w.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z and inversely as the square of w.

Solve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?

Model rational functions: using tables

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as z and the sum of y and w.

Direct Proportion

Joint Variation Examples

Direct Variation / Direct Proportion - Example 2

Direct variation 1 | Rational expressions | Algebra II | Khan Academy

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies directly as the cube root of z and inversely as y.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Combined Variation

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z and inversely as the square root of w.

Joint Variation

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10.

y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.

x varies directly as z and inversely as the sum of y and w.

In Exercises 45–46, describe in words the variation shown by the given equation.

z = k√x / y^2

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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Use Transformations to Graph Rational Functions

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Rational Functions and Their Graphs

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Determine a Quadratic Function's Minimum or Maximum

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