Texas Instruments
Graphs of Rational Functions
Take your kids on a tour of graphing rational functions. Using this TI lesson, high schoolers identify the end behavior of their functions. They find the domain and range, describe end behavior, and look at asymptotes and restrictions of...
Mathematics Vision Project
Module 5: Rational Functions and Expressions
Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...
Virginia Department of Education
Rational Functions: Intercepts, Asymptotes, and Discontinuity
Discover different patterns by making connections between a rational function and its graph. An engaging lesson plan asks scholars to explore the behavior of different rational functions. Groups discover a connection between the...
Curated OER
Discovering Different Types of Functions
Graph polynomials and identify the end behavior of each polynomial function. The class differentiates between linear, quadratic, and other polynomial equations.
EngageNY
Comparing Rational Expressions
Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result.
EngageNY
Rational Exponents—What are 2^1/2 and 2^1/3?
Are you rooting for your high schoolers to learn about rational exponents? In the third installment of a 35-part module, pupils first learn the meaning of 2^(1/n) by estimating values on the graph of y = 2^x and by using algebraic...
EngageNY
Equivalent Rational Expressions
Rational expressions are just fancy fractions! Pupils apply fractions concepts to rational expressions. They find equivalent expressions by simplifying rational expressions using factoring. They include limits to the domain of the...
Curated OER
Do Two Points Always Determine a Linear Function II?
Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.
Mathematics Vision Project
Module 7: Modeling with Functions
The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and...
02 x 02 Worksheets
Inverse Functions
Young mathematicians look for patterns in inverse functions as they relate to the original functions. The comprehensive instructional activity emphasizes vocabulary throughout as well as algebraic and graphical characteristics of the...
Mathematics Vision Project
Module 2: Linear and Exponential Functions
Write, graph, and model all things linear and exponential. Building on the previous module in a nine-part Algebra I series, learners compare linear exponential modeling. They write equations, graph functions, and analyze key features.
Mathematics Vision Project
Module 8: Modeling With Functions
Sometimes there just isn't a parent function that fits the situation. Help scholars learn to combine function types through operations and compositions. Learners first explore a new concept with an introductory activity and then follow...
EngageNY
Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
EngageNY
Solving Rational Equations
What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...
Concord Consortium
Gravity
Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance...
EngageNY
Irrational Exponents—What are 2^√2 and 2^π?
Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...
Curated OER
Exploring Power Functions 2
Young mathematicians learn to write algebraic equations. They solve and graph different polynomial functions with different powers. They then graph radicals and identify the domain and range.
EngageNY
Modeling with Quadratic Functions (part 2)
How many points are needed to define a unique parabola? Individuals work with data to answer this question. Ultimately, they determine the quadratic model when given three points. The concept is applied to data from a dropped...
West Contra Costa Unified School District
Introduction to Logarithms
Build on pupils' understanding of inverse functions by connecting logarithmic functions to exponential functions. This activity allows individuals to see graphically the inverse relationship between an exponential and logarithmic...
Curated OER
Interesting Properties of Cubic Functions to Discover Graphically or Numerically
Learners investigate the slope of a cubic function. They find the tangent line of the cubic function at point P, and discuss the relationship between point P and point Q, the point the tangent line intersects the cubic function. ...
Curated OER
Model Data with Quadratic Functions
Students model data using quadratic equations. In this algebra lesson, students simplify and factor quadratic equations. They graph the function using collected data and analyze the parabola.
EngageNY
A Focus on Square Roots
Pupils learn to solve square root equations and rationalize denominators. Problems include those with extraneous solutions.
EngageNY
Integer Exponents
Fold, fold, and fold some more. In the first installment of a 35-part module, young mathematicians fold a piece of paper in half until it can not be folded any more. They use the results of this activity to develop functions for the area...
Curated OER
Going Back to Your Roots
Who doesn't need to know the Fundamental Theorem of Algebra? Use the theorem to find the roots of a polynomial on a TI calculator. The class explores polynomials with one solution, no real solutions, and two solutions. This less lesson...