Function Rules and Graphing Concepts

This video tutorial covers the representation of functions in various forms, including writing function rules, evaluating functions for given inputs, and representing functions using tables and graphs. It explains the concepts of independent and dependent variables, and demonstrates how to graph linear functions using slope-intercept form. The tutorial also includes practical examples to illustrate these concepts, such as calculating outputs from function rules and graphing functions based on given equations.

What is the role of the independent variable in a function?

• It is always a constant value.

• It does not depend on any other variable.

• It is the output of the function.

• It depends on the dependent variable.

How would you express a function rule where the output is 5 less than the input?

• y = 5x

• y = 5 - x

• y = x - 5

• y = x + 5

If the output is the square of the input, which function rule represents this relationship?

• y = x^2

• y = 2x

• y = x + 2

• y = x - 2

What is the value of y when x = 3 in the function y = 2x + 5?

• 10

• 9

• 11

• 8

Which of the following is a correct representation of a function using a table?

• A table with only x values

• A table with random numbers

• A table with only y values

• A table with x values and corresponding y values

In the equation y = mx + b, what does 'm' represent?

• The x-intercept

• The y-intercept

• The constant term

• The slope of the line

How can you graph a function using slope-intercept form?

• By using only the x-intercept

• By drawing a horizontal line

• By plotting random points

• By plotting the y-intercept and using the slope to find other points

In the context of the carbon dioxide example, what is the dependent variable?

• Gallons of gasoline

• Pounds of carbon dioxide

• The slope of the graph

• The y-intercept

What is the function rule for the relationship between gasoline burned and carbon dioxide produced?

• p = 20g

• p = g + 20

• p = g - 20

• p = 20 + g

Why is the graph of the carbon dioxide function only in the first quadrant?

• Because negative gas values are possible

• Because the graph is a circle

• Because negative carbon dioxide values are possible

• Because you cannot burn a negative amount of gas