Rational Functions and Relationships

The video tutorial teaches how to model rational functions by graphing. It begins with an introduction to rational functions, explaining that they can be represented in the form x times y equals a constant. The tutorial uses a parking cost example to illustrate how the number of people in a van affects the cost per person, demonstrating the inverse relationship. It then explains how to graph these functions, highlighting that the graph approaches but never touches the axes. A real-world problem involving a concrete mixer is used to further illustrate the concept. The tutorial concludes by summarizing the key points of modeling rational functions through graphing.

What is a rational function typically expressed as?

• x + y = k

• x - y = k

• x * y = k

• x / y = k

If parking costs $24 per vehicle, how much does each person pay if there are 3 people in the van?

• $8

• $6

• $12

• $24

What happens to the amount each person pays as the number of people in the van increases?

• It doubles

• It increases

• It decreases

• It stays the same

Why can't the graph of a rational function touch the x or y axis?

• Because the function is linear

• Because the function is quadratic

• Because the function is undefined at zero

• Because the function is exponential

What does the graph of a rational function show as x increases?

• y decreases

• y increases

• y becomes negative

• y remains constant

In the equation x * y = 24, what must be true if x is negative?

• y must be positive

• y must be negative

• y can be any value

• y must be zero

What is each part of the graph of a rational function called?

• Segment

• Branch

• Curve

• Line

What is the equation used to model the concrete mixer problem?

• a + d = 60

• a - d = 60

• a / d = 60

• a * d = 60

At what area will the depth be less than 4 feet in the concrete mixer problem?

• Greater than 20 feet

• Greater than 25 feet

• Greater than 15 feet

• Greater than 10 feet

What does the graph of the concrete mixer problem show about the relationship between area and depth?

• As area increases, depth becomes negative

• As area increases, depth increases

• As area increases, depth decreases

• As area increases, depth remains constant