Understanding Function Behavior and Properties

This video tutorial teaches how to describe the behavior of functions on given intervals by examining graphs. It covers the domain of functions, correct slope calculation, and the importance of reading graphs from left to right. The tutorial explains how graph windows can limit visible data and emphasizes that linear functions have a domain of all real numbers. It also demonstrates how to analyze function behavior, determine constant rates of change, and handle graphs with multiple behaviors.

What is the domain of a function?

• All possible x values

• All possible y values

• All possible z values

• All possible w values

When finding the slope, what should be divided by what?

• Change in z by change in w

• Change in y by change in x

• Change in w by change in z

• Change in x by change in y

How should a graph be read?

• From bottom to top

• From left to right

• From top to bottom

• From right to left

What does the window of a graph represent?

• The function's minimum value

• The entire function

• A limited view of the function

• The function's maximum value

What is the domain of a linear function?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers

What symbol is used to represent infinity?

• A square

• A sideways 8

• A circle

• A triangle

What is the behavior of a function on the interval from negative infinity to zero?

• It increases at a constant rate

• It decreases at a constant rate

• It remains constant

• It fluctuates randomly

How does the function behave on the interval from zero to positive infinity?

• It fluctuates randomly

• It remains constant

• It increases at a constant rate

• It decreases at a constant rate

What is the rate of change for the interval from negative 3 to 0?

• Increases at a rate of 1

• Decreases at a rate of 3

• Decreases at a rate of 1

• Increases at a rate of 3

On the interval from 2 to 4, how does the function behave?

• Decreases at a rate of 2

• Decreases at a rate of 1/2

• Increases at a rate of 2

• Increases at a rate of 1/2