Understanding Linear Functions and Inequalities

This video lecture covers the properties of linear functions, including their definition, graphing, and solving related equations. It explains the slope-intercept form, how to determine if a function is linear, and how to graph linear functions using slope and y-intercept. The lecture also includes examples of solving linear equations and inequalities, and finding the intersection of two linear functions.

What is the general form of a linear function?

• f(x) = a/x

• f(x) = mx + b

• f(x) = ax^2 + bx + c

• f(x) = log(x)

In the slope-intercept form of a linear function, what does 'b' represent?

• The slope

• The x-intercept

• The y-intercept

• The domain

What is the domain of a linear function?

• All real numbers

• Positive integers

• Negative integers

• Non-zero numbers

What does the slope of a linear function represent?

• The maximum value

• The rate of change

• The x-intercept

• The y-intercept

How is the average rate of change calculated for a linear function?

• Change in y over change in x

• Sum of x and y

• Product of x and y

• Change in x over change in y

What does a positive slope indicate about a linear function?

• The function is decreasing

• The function is constant

• The function is increasing

• The function is undefined

What does a slope of zero indicate about a linear function?

• The function is decreasing

• The function is constant

• The function is increasing

• The function is undefined

Why are vertical lines not considered functions?

• They do not pass the vertical line test

• They have no y-intercept

• They have no slope

• They are not linear

How can you determine if a function is linear using a table of values?

• Check if the sum of x and y is constant

• Check if the change in x is constant

• Check if the change in y is constant

• Check if the ratio of change in y to change in x is constant

In the example, why was the function not linear?

• The ratio of change in y to change in x was not constant

• The change in x was not constant

• The function had a vertical line

• The change in y was not constant