Understanding Relationships in Functions

This video tutorial teaches how to model rational functions using tables and graphs. It begins with an introduction to rational functions, explaining their representation as x times y equals a constant. The tutorial uses a parking cost example to illustrate how the number of people affects the cost per person, demonstrating the inverse relationship. It then covers graphing rational functions, highlighting that the graph never touches the axes and can include negative values. Finally, a real-world problem involving a concrete mixer is modeled, showing how the area and depth of concrete are related.

What is the general form of a rational function as introduced in the lesson?

• x / y = k

• x * y = k

• x - y = k

• x + y = k

In the parking cost example, if there are four people in the van, how much does each person pay?

• $12

• $10

• $6

• $8

What does the graph of the parking cost example illustrate about the relationship between the number of people and the cost per person?

• The cost per person remains constant regardless of the number of people.

• The cost per person is unrelated to the number of people.

• As the number of people increases, the cost per person decreases.

• As the number of people increases, the cost per person increases.

Why can't the graph of the parking cost example touch the x or y axis?

• Because no number multiplied by zero can equal the constant.

• Because the graph is a straight line.

• Because the number of people can be zero.

• Because the cost per person can be zero.

What happens to the value of y as x increases in the graph of a rational function?

• y becomes negative

• y remains constant

• y decreases

• y increases

In the context of rational functions, what is a 'branch'?

• A part of the graph that is horizontal

• A part of the graph that is curved and does not touch the axes

• A part of the graph that is linear

• A part of the graph that touches the axes

In the concrete mixing example, what equation models the relationship between area and depth?

• 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 mixing example?

• 15 feet

• 20 feet

• 10 feet

• 25 feet

What does the graph of the concrete mixing example show about the relationship between area and depth?

• As the area increases, the depth decreases.

• The depth remains constant regardless of the area.

• As the area increases, the depth increases.

• The depth is unrelated to the area.

What is the constant in the equation a * d = 60?

• 0

• 60

• d

• a