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 a function rule?

• A rule that describes the relationship between two variables.

• A rule that describes the relationship between two constants.

• A rule that describes the relationship between two graphs.

• A rule that describes the relationship between two equations.

If the output is 5 less than the input, what is the function rule?

• y = x - 5

• y = 5 - x

• y = 5 + x

• y = x + 5

How do you represent the square of the input in a function rule?

• y = 2 + x

• y = x + 2

• y = 2x

• y = x^2

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

• 11

• 8

• 10

• 9

Which form is used to graph a linear equation?

• Slope-intercept form

• Quadratic form

• Exponential form

• Logarithmic form

What is the slope of the line represented by the equation y = -2x + 1?

• 2

• -2

• 1

• -1

How can a function be represented?

• As an equation only

• As a graph only

• As a table only

• As a table, graph, or equation

In the context of carbon dioxide emissions, what does the variable 'g' represent?

• Liters of gasoline

• Miles driven

• Pounds of carbon dioxide

• Gallons of gasoline

What is the function rule for carbon dioxide emissions based on gasoline consumption?

• p = g - 20

• p = 20g

• p = g + 20

• p = 20 + g

Why is the graph of the function p = 20g only drawn in the first quadrant?

• Because the graph is a circle

• Because the graph is a parabola

• Because negative carbon dioxide emissions are possible

• Because negative gas consumption is not possible