Modeling Rational Functions by Graphing

The video tutorial explains how to model rational functions by graphing. It begins with an introduction to rational functions, often expressed as x times y equals a constant. The tutorial uses a parking cost example to illustrate how the cost per person decreases as the number of people increases, demonstrating the inverse relationship. It also covers graphing these functions, showing that the graph approaches but never touches the axes. The tutorial concludes with a concrete mixer problem, modeling the relationship between area and depth using a rational function.

What happens to the cost per person when more people share the parking fee?

• The cost per person increases.

• The cost per person decreases.

• The cost per person doubles.

• The cost per person remains the same.

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

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

• Because the graph is a straight line.

• Because the graph is a parabola.

• Because the graph is a circle.

What is a branch in the context of a rational function graph?

• A part of the graph that forms a straight line.

• A separate section of the graph that does not touch the axes.

• A part of the graph that touches the y-axis.

• A part of the graph that touches the x-axis.

In the concrete mixer problem, what happens to the depth when the area is greater than 15 feet?

• The depth is zero.

• The depth is more than four feet.

• The depth is less than four feet.

• The depth is exactly four feet.

How can the relationship between area and depth in the concrete mixer problem be modeled?

• Using a linear equation.

• Using an exponential function.

• Using a quadratic equation.

• Using a rational function.