Function Behavior and Representation

This video tutorial covers the first free response question (FRQ) on the AP Pre-Calculus exam. It explains the structure and expectations of the FRQ, including the use of a graphing calculator and the types of function concepts involved. The video provides a detailed analysis of an example problem from the course exam description, breaking down each part of the problem and demonstrating how to solve it. The tutorial emphasizes the importance of understanding function composition, inverse functions, and end behavior using limit notation. It also guides students in determining the best model for a function using table values.

What is the main focus of the first free response question on the AP Pre-Calculus exam?

• Graphing functions

• Calculating derivatives

• Solving equations

• Understanding function concepts

Which of the following is NOT a type of function representation mentioned in the video?

• Algebraic

• Graphical

• Analytical

• Numerical

In the example problem, what form is the function G presented in?

• Tabular

• Numerical

• Analytical

• Graphical

What is the first step in solving Part A of the example problem?

• Identify zeros of the function

• Calculate the value of H at 5

• Find the inverse of function f

• Determine the end behavior of G

What is the correct value of H(5) in the example problem?

• 3.88

• 34

• 5

• 177.86

In Part B, what is the x-value where G(x) equals 3?

• 4.875

• 3.875

• 5.875

• 2.875

What is the end behavior of G as x decreases without bound?

• Positive infinity

• Negative infinity

• Zero

• Undefined

Which type of function is best modeled by the table values of f(x) in Part C?

• Exponential

• Quadratic

• Linear

• Logarithmic

What is the reason for identifying the function as quadratic in Part C?

• Constant first difference

• Constant second difference

• Proportional outputs

• Proportional inputs