Algebraic Expressions and Variations

The video tutorial covers various mathematical concepts including direct and joint variation, graphing functions and identifying asymptotes, operations with polynomials, and solving equations using cross-multiplication. The instructor provides examples and explanations to help students understand these topics, emphasizing the importance of practice and review.

What is the main focus of the review session?

• To discuss historical events

• To prepare for a science test

• To review previously learned material

• To introduce new mathematical concepts

In a direct variation, if y = 5 when x = 1, what is the constant of variation?

• 10

• 1

• 0

• 5

What is the equation for y in terms of x if y varies directly with x and y = 5 when x = 1?

• y = x + 5

• y = x/5

• y = 5/x

• y = 5x

If z varies jointly with x and y, and z = -75 when x = 3 and y = -5, what is the constant of variation?

• 5

• -15

• -5

• 15

What is the equation for z in terms of x and y if z varies jointly with x and y and the constant of variation is 5?

• z = 5xy

• z = 5/x + y

• z = x + 5y

• z = 5/x - y

What is the first step in graphing a function to find its asymptotes?

• Plot random points

• Calculate the y-intercepts

• Find the x-intercepts

• Determine the vertical asymptotes

Where is the vertical asymptote located for the function f(x) = (3x - 2)/(x - 4)?

• x = 0

• x = -4

• x = 4

• x = 3

What is the horizontal asymptote for the function f(x) = (3x - 2)/(x - 4)?

• y = 4

• y = 3

• y = 0

• y = -2

What is the degree of the numerator in the function f(x) = (3x - 2)/(x - 4)?

• 0

• 3

• 2

• 1

What is the degree of the denominator in the function f(x) = (3x - 2)/(x - 4)?

• 3

• 0

• 2

• 1