Standard: HSF.IF.C9 – Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Grade level: High School: Functions
Subject: Mathematics
Domain: Interpreting Functions
Teacher Overview
This standard emphasizes the ability to compare functions represented in different forms. It is crucial for developing a deeper understanding of functions and their properties, which is foundational for higher-level math topics. Students should be comfortable with interpreting graphs, solving algebraic equations, and understanding basic function properties.
Mastery of this standard will enable students to tackle more complex functions and understand advanced topics in calculus, such as limits and derivatives.
Common Misconception 1
A common misconception is that functions represented differently, such as a graph and an equation, cannot be compared. This is incorrect because all representations convey the same underlying mathematical relationship.
Intervention 1
To address this, present students with the same function in different forms and guide them in identifying equivalent properties, such as intercepts and maximum points.
Common Misconception 2
Another misconception is that the maximum or minimum points are the only significant features of a function. This overlooks other important aspects such as intercepts and intervals of increase/decrease.
Intervention 2
Use diverse examples to illustrate the importance of other function features, and engage students in activities that require them to identify and compare these features.
Prerequisite Knowledge
Students should understand basic function properties, be able to read and interpret graphs, and have foundational skills in algebraic manipulation.
Subsequent Knowledge
Students will develop the ability to analyze more complex functions, understand transformations, and apply these skills to calculus topics such as limits and derivatives.
Instructional Activities
- Graphing different functions and comparing their properties
- Using tables to analyze numerical data of functions
- Interpreting verbal descriptions and converting them into algebraic expressions
- Collaborative group work to compare and contrast functions in different forms
