Understanding Function Properties and Behavior

This video provides a comprehensive review of Unit One in AP Pre-Calculus, focusing on polynomial and rational functions. Key topics include understanding zeros, analyzing function values, exploring increasing and decreasing functions, and examining concavity and rate of change. The video also covers end behavior using limit notation, transformations of functions, and techniques for solving equations. The aim is to equip students with the essential concepts needed to succeed in the AP Pre-Calculus exam.

What is the primary focus of Unit 1 in AP Pre-Calculus?

• Trigonometric functions

• Polynomial and rational functions

• Exponential growth

• Logarithmic functions

What is a zero of a function?

• A point where the function has a maximum

• A value of x that makes the function's output zero

• A value of x that makes the function's output one

• A point where the function is undefined

How can you determine where a function is positive on a graph?

• By finding where the graph is below the x-axis

• By checking where the graph intersects the y-axis

• By looking at the slope of the graph

• By identifying where the graph is above the x-axis

What does it mean for a function to be increasing on an interval?

• The function's output decreases as the input decreases

• The function's output increases as the input increases

• The function's output remains constant as the input increases

• The function's output decreases as the input increases

What is an absolute extrema?

• A point that is higher than all other points in its vicinity

• A point that is lower than all other points in its vicinity

• A point that is neither a maximum nor a minimum

• A point that is the highest or lowest in the entire function

What does concavity describe in a function?

• The overall shape of the graph

• The rate of change of the function

• The direction in which the function is moving

• The intervals where the function is increasing

How do you calculate the average rate of change of a function?

• By calculating the area under the curve

• By finding the slope of the tangent line

• By dividing the change in output by the change in input

• By finding the difference between the maximum and minimum values

What does the end behavior of a function describe?

• The behavior of the function as x approaches infinity

• The behavior of the function as x approaches zero

• The points where the function intersects the axes

• The intervals where the function is concave up

What is a vertical dilation in function transformations?

• A stretch or shrink of the graph vertically

• A shift of the graph up or down

• A shift of the graph left or right

• A reflection across the x-axis

What is the first step in solving an equation without a calculator?

• Find the derivative

• Graph the function

• Use a calculator to find the solution

• Set the equation equal to zero