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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...
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Exploring Vertical Asymptotes
Scholars identify the domain of a rational function in this precalculus lesson plan. They identify the removable discontinuity and label what will make the denominator zero. Learners also describe properties of the graph as it relates to...
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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.
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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...
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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.
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Rational Functions
Through a mini assessment, high schoolers 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...
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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,...
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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.
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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...
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Rational Functions
In this algebra worksheet, students solve rational functions and identify the x and y intercepts, the vertical and horizontal asymptotes. There are 26 questions.
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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.
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Reciprocals of Quadratic Functions
Eleventh graders investigate inverse functions. For 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.
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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...
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Worksheet 9, Rational Functions
In this algebra worksheet, students tell how they would find the domain of a rational function. They find the intercepts of a rational function and graph it. Students test for symmetry, locate the asymptotes and determine where the graph...
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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...
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Worksheet 5 - Squeeze Theorem
For this Squeeze Theorem worksheet, students compute limits, identify a graph that represents the Squeeze Theorem, and graph given functions. This two-page worksheet contains seven multi-step problems.
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Arithmetic Complex Numbers
Students convert quadratic functions from standard form to vertex form. In this algebra lesson plan, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
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Trigonometry Practice: Trigonometric Graphs #3
In this Trigonometry Practice worksheet, students are asked to graph a variety of trigonometric functions. A graphing calculator is required to complete these three pages.
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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...
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Polynomials Functions
High schoolers factor polynomials and linear functions and apply concepts of the fundamental theorem of algebra to solve problems. They graph their solutions and analyze the graph.
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Rational Function Graphs
Students use algebraic methods to represent and solve problems. Using a graphing calculator, students solve rational and inequality problems. They visually demonstrate solutions of functions through graphing. Students answer questions...
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Roller Coaster Robot
Pupils calculate the area under a curve. In this calculus lesson, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
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Rational Functions
Learners evaluate rational functions. In this precalculus lesson, students make observations and define what makes a rational function and what makes a linear function. They use the Ti calculator to visualize the different graphs.
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Nearpod: Rational Functions: Asymptotes & Graphing
In this lesson, students will learn how to find holes, vertical asymptotes, and horizontal asymptotes graphically and algebraically.