Algebra 2: Rational Functions and Variations

The video tutorial covers Chapter 5 of Algebra 2, focusing on graphing and solving rational functions. It introduces inverse variation as a key concept, followed by a review of direct variation from Algebra 1. The tutorial also explains joint variation, combining direct and inverse variations. The lesson emphasizes understanding these variations through examples and exercises, preparing students for quizzes and tests.

What is the main focus of Chapter 5 in Algebra 2?

• Graphing and solving linear equations

• Graphing and solving rational functions

• Solving quadratic equations

• Understanding polynomial functions

In direct variation, if y = ax, what does 'a' represent?

• The slope of the line

• The x-intercept

• The y-intercept

• The constant of variation

Which of the following is an example of direct variation?

• y = 1/x

• y = x^2

• y = 5x

• y = 3x + 2

In inverse variation, what happens to y as x increases?

• y becomes zero

• y remains constant

• y decreases

• y increases

How do you determine if a relationship is an inverse variation?

• By checking if y = ax

• By checking if y = x^2

• By checking if y = a/x

• By checking if y = x + a

What is the first step in writing an inverse variation equation?

• Identify the constant of variation

• Graph the equation

• Write the equation y = a/x

• Solve for x

If x and y vary inversely, and x = 4 when y = 6, what is the constant of variation?

• 24

• 18

• 12

• 10

In joint variation, if z varies jointly with x and y, how is it expressed?

• z = a/x - y

• z = a + xy

• z = axy

• z = a/x + y

What is a key characteristic of joint variation?

• It does not involve a constant

• It is always linear

• It combines direct and inverse variations

• It involves only one variable

If r varies jointly as j squared and the square root of 2, and inversely as s cubed, how is it expressed?

• r = aj^2s^3√2

• r = a√2/j^2s^3

• r = aj^2s^3/√2

• r = aj^2√2/s^3