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Assessment
Mt. San Antonio Collage

Test 2: Rationals, Exponentials, and Logarithms

For Students 9th - 12th Standards
Running out of logarithm questions in class? The nicely organized two-page worksheet provides practice in rational, logarithmic, and exponential functions. All the topics include graphing, solving, and finding domain and range. 
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Assessment
Mt. San Antonio Collage

Quiz 2: Types of Functions

For Students 9th - 12th Standards
Here is a resource that provides the structure of an assessment with the convenience of a full answer key. The focus is on rational, exponential, and logarithm functions with a few questions on solving polynomials. 
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Worksheet
Mt. San Antonio Collage

Graphs of Rational Functions

For Students 9th - 12th Standards
Sometimes graphing rational functions can feel a little "irrational." Starting with the basics, learners work their way through the pieces of these graphs and finish off with an application question. 
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Lesson Plan
Curated OER

Is There a Limit to Which Side You Can Take?

For Teachers 9th - 12th Standards
Calculus high schoolers find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise...
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Lesson Plan
K20 Learn

Driving Rationally: Introduction To Rational Functions And Asymptotes

For Teachers 11th Standards
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...
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AP Test Prep11:15
2
2
Flipped Math

Calculus AB/BC - Exploring Types of Discontinuities

For Students 10th - 12th
Continue one's studies by studying discontinuities. The 11th of 18 lessons in Unit 1 - Limits and Continuity first describes the different types of discontinuities. By watching a video, pupils learn to algebraically determine the...
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AP Test Prep13:27
1
1
Flipped Math

Calculus AB/BC - Limits at Infinity and Horizontal Asymptotes

For Students 10th - 12th
Learning about end behavior means it's close to the end of the unit. The 16th of 18 lessons in Unit 1 - Limits and Continuity has scholars watch a video to learn how limits at infinity can be used to determine horizontal asymptotes and...
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AP Test Prep7:55
1
1
Flipped Math

Calculus AB/BC - Infinite Limits and Vertical Asymptotes

For Students 10th - 12th
Infinite limits just got infinitely more interesting. The 15th of 18 installments in Unit 1 - Limits and Continuity looks at infinite limits and vertical asymptotes of rational functions. Scholars review how to determine the locations of...
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AP Test Prep6:45
1
1
Flipped Math

Calculus AB/BC - Removing Discontinuities

For Students 10th - 12th
It's called a removable discontinuity for a reason. After reviewing the conditions for a removable discontinuity to exist, scholars watch an informative video to learn how to remove the discontinuity. They look at several examples...
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Assessment
EngageNY

End-of-Module 3 Assessment Task

For Teachers 11th - 12th Standards
Let's see what the class learned! The last installment of the 23-part Pre-calculus module consists of nine assessment questions designed to measure a specific portion of a standard in the unit. Learners demonstrate their understanding of...
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Lesson Plan
EngageNY

Horizontal and Vertical Asymptotes of Graphs of Rational Functions

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

Graphing Rational Functions

For Teachers 11th - 12th Standards
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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Lesson Plan
EngageNY

End Behavior of Rational Functions

For Teachers 11th - 12th Standards
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
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Lesson Plan
EngageNY

Rational Functions

For Teachers 11th - 12th Standards
Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...
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Lesson Plan
EngageNY

Transforming Rational Functions

For Teachers 11th - 12th Standards
Move all rational functions—well, maybe. Learners investigate the graphs of the reciprocals of power functions to determine a pattern between the graph and the power. Pupils graph rational functions where transformations are clearly...
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Unit Plan
Radford University

Function Family Fun

For Teachers 9th - 12th Standards
It's time for a family reunion—function families, that is. Pupils first review different types of parent functions. They then see how to apply transformations to graphs and learn how to select the most appropriate type of function to...
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eBook
Rice University

College Algebra

For Students 9th - Higher Ed Standards
Is there more to college algebra than this? Even though the eBook is designed for a college algebra course, there are several topics that align to Algebra II or Pre-calculus courses. Topics begin with linear equation and inequalities,...
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eBook
Rice University

Precalculus

For Students 11th - Higher Ed Standards
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
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eBook
Rice University

Algebra and Trigonometry

For Students 10th - Higher Ed Standards
Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...
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Assessment
Concord Consortium

Rational and Not So Rational Functions

For Students 11th - 12th Standards
Do not cross the line while graphing. Provided with several coordinate axes along with asymptotes, pupils determine two functions that will fit the given restrictions. Scholars then determine other geometrical relationships of asymptotes...
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Assessment
Concord Consortium

Symbolic Similarity

For Students 9th - 11th Standards
How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...
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Unit Plan
Mathematics Vision Project

Module 5: Rational Functions and Expressions

For Students 10th - 12th Standards
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...
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Assessment
Concord Consortium

Gravity

For Students 9th - 11th Standards
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 from...
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Assessment
Concord Consortium

Transformations Resource

For Students 9th - 12th Standards
Transform your lesson for transforming functions. Scholars transform linear, quadratic, exponential, rational, and trigonometric expressions. They write their expressions to fit specific forms and identify the values of the resulting...