Function Rules and Graphing Concepts

This video tutorial covers the representation of functions in various forms, including equations, tables, and graphs. It explains how to write function rules, evaluate functions for given inputs, and graph linear functions using slope-intercept form. The tutorial also discusses the relationship between independent and dependent variables and provides examples to illustrate these concepts.

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

• It depends on the dependent variable.

• It is the output of the function.

• It does not depend on any other variable.

• It is always a constant value.

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

• y = x + 5

• y = 5 - x

• y = 5x

• y = x - 5

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

• y = x - 2

• y = x + 2

• y = 2x

• y = x^2

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

• 11

• 9

• 8

• 10

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

• A table with only x values

• A table with only y values

• A table with x values and corresponding y values

• A table with random numbers

In the slope-intercept form y = mx + b, what does 'm' represent?

• The y-intercept

• The slope of the line

• The x-intercept

• The constant term

How can you graph the function y = -2x + 1 using a table of values?

• By calculating y for selected x values and plotting the points

• By plotting random points

• By using only positive x values

• By drawing a horizontal line

What is the function rule for a car producing 20 pounds of CO2 per gallon of gasoline burned?

• p = 20g

• p = g + 20

• p = g - 20

• p = 20 + g

In the context of the car's CO2 emissions, what does the slope of the function represent?

• The initial amount of CO2

• The total CO2 produced

• The amount of gasoline burned

• The amount of CO2 produced per gallon

Why is the graph of the car's CO2 emissions function only in the first quadrant?

• Because the function is not linear

• Because CO2 emissions can be negative

• Because the graph is a straight line

• Because gasoline consumption cannot be negative