Understanding Average Cost and Horizontal Asymptotes

The video tutorial explains how to calculate the average cost of producing smoke shifters using a given function. It covers evaluating the cost for 12 units, determining the production level needed to reduce the cost to $11, and finding the horizontal asymptote of the cost function. The tutorial uses both algebraic and graphical methods to solve these problems, providing a comprehensive understanding of cost functions and asymptotic behavior.

What is the average cost to produce 12 smoke shifters?

• $18.25

• $17.00

• $16.42

• $15.50

How many smoke shifters must be produced to reduce the average cost to $11 each?

• 20

• 30

• 22

• 25

What is the first step in solving the equation to find the number of smoke shifters needed for a specific average cost?

• Subtract 125 from both sides

• Multiply both sides by X

• Add 6X to both sides

• Divide both sides by 11

What does a horizontal asymptote represent in the context of this problem?

• The cost of producing one additional unit

• The maximum cost of production

• The minimum cost of production

• The average cost as production increases indefinitely

Which tool is used to find the horizontal asymptote graphically?

• A ruler

• A graphing calculator

• A protractor

• A spreadsheet

What is the horizontal asymptote of the average cost function?

• y = 5

• y = 6

• y = 7

• y = 8

How do you determine the horizontal asymptote by analyzing the function?

• By dividing the constant terms

• By finding the sum of coefficients

• By subtracting the coefficients

• By comparing the degrees of the numerator and denominator

What happens to the average cost as the number of smoke shifters produced increases indefinitely?

• It decreases to $0

• It approaches $6

• It remains constant at $11

• It increases to $10

If the degree of the numerator is higher than the denominator, what is the horizontal asymptote?

• y = 6

• y = 0

• y = 1

• There is no horizontal asymptote

What is the ratio of the leading coefficients in the average cost function?

• 8/1

• 7/1

• 6/1

• 5/1