Curated OER
Hyperbolas: Sketching from the Equation
In this algebra worksheet, young scholars sketch graphs of hyperbolas after solving equations to standard form and interpreting the center, vertices, foci, axis, asymptotes, and eccentricity from the equation. There are 58 questions.
Curated OER
Worksheet 7 - Asymptote
In this asymptote worksheet, students compute limits, graph vertical asymptotes, and find the slope of the secant line. This one-page worksheet contains six multi-step worksheets.
Curated OER
Graphing Quadratic Equations
Review the form of a quadratic function, and the parabola it creates. Continue on with the whole group to work through a mini-lab, practicing how to graph quadratic equations with one variable. The goal of this activity is for the group...
K20 LEARN
Driving Rationally: Introduction To Rational Functions And Asymptotes
Calculating average speeds is not as simple as finding an average. The lesson introduces class members to rational functions by presenting a problem about finding an average speed for the rest of a trip. Pupils develop an equation to...
Curated OER
Asymptotes and Zeros
Learn how to explore rational functions and investigate the graphs rational functions and identify its singularities and asymptotes. High schoolers approximate the solutions to rational equations and inequalities by graphing.
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...
Curated OER
The Canoe Trip, Variation 2
The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...
Curated OER
Exploring Vertical Asymptotes
Scholars identify the domain of a rational function in this precalculus lesson. They identify the removable discontinuity and label what will make the denominator zero. Learners also describe properties of the graph as it relates to the...
EngageNY
Curves from Geometry
Escape to investigate hyperbolas. Pupils take a look at what happens to the elliptical orbital path of a satellite that exceeds escape velocity as the opener to the eighth lesson in a unit of 23. Scholars analyze basic hyperbolas and how...
Curated OER
A Slant Asymptote
In this slant asymptote worksheet, students solve 1 rational equation. Students determine the slant asymptote of a rational equation.
Curated OER
Asymptotes And Zeros of Rational Functions
Budding mathematicians graph polynomial functions and examine their zero and y-intercepts. They analyze how the zero and y-intercepts of the numerator and denominator affect the graph of a rational function. Several great additional...
Curated OER
The Canoe Trip, Variation 1
Your river sportsmen will explore an example of paddling upstream as they build functions modeling speed and time in terms of the speed of the current. They then use their algebraic models to interpret features of the function related to...
Curated OER
Matchstick Math: Using Manipulatives to Model Linear, Quadratic, and Exponential Functions
Playing with matches (unlit, of course) becomes an engaging learning experience in this fun instructional unit. Teach pupils how to apply properties of exponential functions to solve problems. They differentiate between quadratic and...
Curated OER
Reciprocals of Quadratic Functions
Eleventh graders investigate inverse functions. In this Algebra II lesson, 11th graders use their prior knowledge of linear, exponential,and quadratic functions to create a graph of an equation they have never seen before.
Curated OER
Exponential Equations and Functions
In this college level Pre-Calculus worksheet, students solve problems involving exponential functions. Students determine the domain, range, y-intercept and asymptotes of exponential functions. The three page worksheet contains seventy...
Curated OER
Hyperbolas
Students locate and identify the center, foci, vertices, and asymptotes fo hyperbolas. They graph equations involving asymptotes and hyperbolas. Finally, students determine the equation of a hyperbola with a horizontal transverse axis.
Curated OER
Worksheet #12 - Logarithms
In this worksheet, students convert exponential expressions into an equivalent logarithm and visa versa. They find the exact value of logarithmic expressions and determine the domain of a given function. Finally, students use...
Curated OER
Similarities and Differences in Properties of Different Families of Functions - An Investigation
Exploring families of functions allows students compare and contrast properties of functions. Students discuss properties that include symmetry, max and min points, asymptotes, derivatives, etc.
Virginia Department of Education
Exponential Modeling
Investigate exponential growth and decay. A set of six activities has pupils collecting and researching data in a variety of situations involving exponential relationships. They model these situations with exponential functions and solve...
Curated OER
Graph Logarithms
Mathematicians graph logarithmic equations. Teach your students how to identify the intercepts of logarithmic equations and tell whether the function is increasing or decreasing. They find the domain and range of each function.
Curated OER
Parabolas
In this algebra worksheet, students solve parabolas using the standard and vertex forms. They find the vertex and asymptote and graph the parabola. There are 64 problems.
Curated OER
Exploring the Witch of Agnesi
students construct the graph of the Witch of Agnesi, and investigate both its asymptotes and inflection points. They construct the graph of the Witch of Agnesi and conjecture the asymptotes and inflection points of the function. ...
Curated OER
Worksheet 8, Exponents
In this calculus worksheet, students analyze one equation by finding the maximum number of zeros. They use Descarte's Rule of Signs and the rational roots theorem. Students use synthetic division to factor the polynomial. Students solve...
Curated OER
Roller Coaster Robot
Students calculate the area under a curve. In this calculus instructional activity, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.