Identifying Functions and Their Models

This video tutorial covers the selection and application of linear, quadratic, and exponential models for data analysis. It begins with an introduction to these models, followed by detailed explanations of quadratic, linear, and exponential functions, including their forms and graphical representations. The tutorial then demonstrates how to analyze data using these models by examining differences and ratios. Finally, it applies this knowledge to a real-world scenario, modeling the depreciation of a car's value over time using an exponential function.

Which of the following is the standard form of a quadratic function?

• y = a / (bx + c)

• y = mx + b

• y = ax^2 + bx + c

• y = a * b^x

What does the graph of a linear function look like?

• A circle

• A curve that grows or decays

• A straight line

• A parabola

In Example 1, Part A, what type of model is identified by the graph of the five coordinate points?

• Linear

• Quadratic

• Exponential

• None of the above

In Example 1, Part B, why is the model identified as exponential?

• The points form a curve that does not decrease by the same amount each time

• The points form a parabola

• The points form a circle

• The points form a straight line

How can you identify a linear function from a table of values?

• The x-values have a common difference

• The x-values have a common ratio

• The y-values have a common ratio

• The y-values have a common difference

What indicates a quadratic function when looking at the differences in a table of values?

• The first differences are constant

• The x-values have a common ratio

• The y-values have a common ratio

• The second differences are constant

In Example 2, Part A, what type of function is identified by the data?

• Linear

• None of the above

• Exponential

• Quadratic

In Example 2, Part B, why is the model identified as quadratic?

• The first differences are constant

• The second differences are constant

• The y-values have a common ratio

• The x-values have a common ratio

In Example 3, what type of function best models the value of a used car over time?

• None of the above

• Exponential

• Quadratic

• Linear

What is the decay factor for the value of the used car in Example 3?

• 1.12

• 0.88

• 1.25

• 0.75