EngageNY
Horizontal and Vertical Asymptotes of Graphs of Rational Functions
Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...
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.
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 instructional activity asks scholars to explore the behavior of different rational functions. Groups discover a connection between...
Curated OER
Asymptotes and Zeros
Learn how to explore rational functions and investigate the graphs rational functions and identify its singularities and asymptotes. Students approximate the solutions to rational equations and inequalities by graphing.
Curated OER
Rational Functions
Through a mini assessment, students identify and list the vertical and horizontal asymptotes for the given rational functions and determine the type of asymptote of a given rational function. They also decide which form of a function...
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
Hyperbolas: Sketching from the Equation
In this algebra worksheet, learners 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
Exploring Vertical Asymptotes
Scholars identify the domain of a rational function in this precalculus activity. They identify the removable discontinuity and label what will make the denominator zero. Learners also describe properties of the graph as it relates to...
Curated OER
Crossing the Asymptote
Students investigate graphs and their asymptotes. In this precalculus lesson, students examine the numerator and denominator of their rational functions. This helps them identify where and when the graph will cross its asymptote.
Curated OER
Worksheet 28 - Functions
In this function worksheet, students identify functions which are their own derivative. They determine the vertical and horizontal asymptotes of functions. This one-page worksheet contains seven multi-step problems.
EngageNY
Graphing Rational Functions
Put everything together in a picture. Scholars take what they learned in the previous three lessons in the 15th segment of a 23-part unit to graph rational functions. They find the end behavior, the horizontal and vertical asymptotes if...
Curated OER
A Slant Asymptote
In this slant asymptote worksheet, learners solve 1 rational equation. Students determine the slant asymptote of a rational equation.
K20 LEARN
Driving Rationally: Introduction To Rational Functions And Asymptotes
Calculating average speeds is not as simple as finding an average. The instructional activity introduces class members to rational functions by presenting a problem about finding an average speed for the rest of a trip. Pupils develop an...
Curated OER
Graphing Rational Functions
Learners complete an activity, included, of the information on asymptotes and intercepts. They also solve and complete eight questions on graphing rational functions, file included. Finally, pupils summarize vertical asymptotes,...
Curated OER
Worksheet 4 - function
In this function worksheet, students identify functions, express decimals as fractions and write decimals as a geometric series. This one-page worksheet contains six multi-step problems.
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
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
Rational Functions
In this algebra worksheet, young scholars solve rational functions and identify the x and y intercepts, the vertical and horizontal asymptotes. There are 26 questions.
Curated OER
Intuitive Approach to Limits
Students identify and comprehend the concept of limit in mathematics. They also view artistic works illustrating limits by M. C. Escher and apply techniques of one-sided limits to graphs of relations. Finally, students compute limits...
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
Hyperbolas
Students engage in a lesson that covers the concepts related to the graphing of hyperbolas looking at topics like foci, center, vertices, and asymptotes. They find multiple different points in the coordinate plain and then plot the graph.
Curated OER
Worksheet 4: Limits
In this limits worksheet, students evaluate limits and graph given expressions. They classify graphs as removable discontinuities, jump discontinuities, or asymptotes. this two-page worksheet contains seven multi-step problems.
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.
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...
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