Understanding Function Rules and Graphs

This video tutorial covers the representation of functions in various forms, including writing function rules, evaluating functions for specific 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.

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 equations

• A rule that describes the relationship between two graphs

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

• y = 5 - x

• y = x + 5

• y = x - 5

• y = 5 + x

What is the function rule for when the output is the square of the input?

• y = 2x

• y = x^2

• y = x - 2

• y = x + 2

How do you evaluate the function y = 2x + 5 when x = 3?

• y = 8

• y = 10

• y = 11

• y = 9

What is the slope-intercept form of a linear equation?

• y = x + mb

• y = b + mx

• y = mx + b

• y = m + bx

How can a function be represented?

• As a table, graph, or equation

• As a graph only

• As a table only

• As an equation only

What is the slope of the function y = -2x + 1?

• -2

• 2

• 1

• -1

In the real-world example, what does the variable 'g' represent?

• Liters of water

• Miles driven

• Pounds of carbon dioxide

• Gallons of gasoline

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

• p = 20g

• p = g + 20

• p = g - 20

• p = 20 + g

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

• Because negative gas consumption doesn't make sense

• Because the graph is a circle

• Because the graph is a parabola

• Because the graph is a hyperbola