# Ch 3: Common Core HS Functions - Graphing

Allow our lessons to help you meet the requirements for the Common Core as you educate your class on graphing. You'll learn how to recognize when your students have fully grasped the standard, and you'll also receive suggestions about how you can better teach the lessons in your classroom.

Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (CCSS.Math.Content.HSF-IF.B.4)

Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (CCSS.Math.Content.HSF-IF.B.5)

Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (CCSS.Math.Content.HSF-IF.B.6)

Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima. (CCSS.Math.Content.HSF-IF.C.7a)

A full comprehension of graphing allows students to adequately explain the relationships that exist in graphs and look at a graph to see how often a function changes. Students who understand the elements of graphing can recognize the most important features on a graph and will be able to connect a domain function to a graph. The lessons found in this standard include the following topics:

• The different parts of a graph
• Graphs as relationships between quantities
• Sketching graphs from tables or verbal descriptions of relationships
• Connecting domains to graphs of functions
• Find the average rate of change from a graph or table
• Calculate the average rate of change from an equation
• Graphs of equations as sets of solution points

Your students show they've mastered this standard by identifying the elements of a graph, using graphs to show the connections shared by quantities, and making graphs from listening to a description of a relationship. The combination of the standard and the lessons can help students get ready for higher education and jobs related to investment banking, aerospace or mechanical engineering, drafting, optometry and more.

### How to Use These Lessons in Your Classroom

To get your students involved and more interested in graphing, you can employ the engaging video lessons related to these tips:

#### Utilize Different Learning Approaches

When you get to the Graphs as Relationships Between Quantities lesson, have your students draw out those relationships and write a short one- or two-sentence description about the pictured relationship. This is a good way to further engage students and can help them better understand the relationships they're learning about.

#### Have Students Sketch Graphs

Give your class verbal descriptions of graphs and have them draw them out. You could also group students and appoint one person in each group to describe a graph while the others draw them. If you like, you can include these with the lesson quizzes or have students complete them for extra points.

#### Make Real-World Connections

Have your students think of ways that they can use graphing in their day-to-day lives. Students might feel as though they'll never use what they're learning in real life, so show them that math can be just as useful outside of the classroom as it can inside of it. Give them a few examples of relevant industries and see if they can come up with specific occupations and how graphing would be used.

1 Lesson in Chapter 3: Common Core HS Functions - Graphing
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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