4. Polynomial and Rational Functions

Solve Direct Variation Problems

Modeling Using Variation

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

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

Joint and Combined Variation

Direct Variation / Direct Proportion - Example 2

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 Long Division to Divide Polynomials

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Determine a Quadratic Function's Minimum or Maximum

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