Algebraic Function Teacher Resources
Find Algebraic Function educational ideas and activities
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Graphs of Quadratic Functions
After making a correction to the last problem in his previous video, Sal explains how to graph quadratic functions. Those who have a hard time with the concept of graphing algebraic functions will find Sal's instruction and easygoing manner a welcome change from staring at textbooks.
Functions Part 2
This video continues to look at evaluating functions by looking at examples of evaluating basic composite functions.
Exploring the Vertex Form of the Quadratic Equation
Students explore the concept of quadratic equations. In this quadratic equations lesson, students graph parabolas on their calculator and determine the vertex form of the function given the graph. Students examine the vertex of the parabolas and which way the parabola opens.
Inverse Trig Functions: Arctan
Continuing with inverse trigonometric functions, Sal finds the value for tan^-1-1. He also shows the restricted domain of the arctan function.
Linear and Nonlinear Functions
Students identify properties of a line. In this algebra lesson, students differentiate between functions and nonfunctions. They use the slope and y intercept to graph their lines.
Functions in Motion
Students graph polynomials functions and analyze the end behavior. In this algebra lesson, student differentiate between the different polynomials based on the exponents. They use a TI to help with the graphing.
Introduction to Function Inverses
Starting from a brief look at functions and the mapping of domains to ranges, Sal starts out with an intuitive sense of what a function inverse is. He then, using an example, shows how to find the inverse of a function and also shows how the graph of the function and its inverse are reflections over the y = x line. This video provides a good review of function inverses for more advanced students or a nice introduction for the beginning student.
Connection between even and odd numbers and functions
Are odd numbers connected to odd functions and even numbers to even functions? This video tries to clarify that connection. It also talks about functions that are neither odd nor even to give a more intuitive feeling about classifying these functions.
Functional Relationships 1
What does it mean for two things to have a functional relationship? In this video, Sal takes the example of a table of values that map a personÕs name to their height and discusses how this is a functional relationship. He also considers how the table could be changed so that the relationship is no longer a function.
Domain of a Function
We look at a number of different examples of functions and see what their domain is. Sal writes the domain in set notion and shows how different functions can have different input values that cause the function to be undefined.
Ex: Constructing a Function
This video explores a basic linear cost equation. Given a rate-per-photo and a fixed-one time cost, write a function that represents the amount a customer would pay for x number of photos.
This is a wonderful exercise for learners to apply their critical thinking skills along with their knowledge of quadratic functions and parabolas. Young mathematicians investigate a real-world scenario about the height a baseball reaches when it is thrown. They compare two different representations, a graph and an equation, of the height as a function of time. Answering the three questions the activity poses requires finding the vertex and roots of a quadratic equation using a method of choice and interpreting the solutions within the context of the problem. The exercise can be used for assessment or practice.
Domain and Range 1
After defining a simple function from a word problem, this video, shows how one could find the domain and the range of that function. The goals here are to reinforce the definitions of domain and range with a concrete example.
Renting Cars, Stealing Money, and Linear Functions
When comparing pricing models, young mathematical consumers, create linear equations and analyzing them graphically and algebraically. They look at the meaning of slope and intercepts, as well as the intersection points of lines.
High schoolers are introduced to the techniques associated with interpreting functions. The vocabulary associated with this technique is reviewed, then pupils view a PowerPoint (embedded in the plan), that shows how to interpret functions. Learners then break into four groups and complete the assignments given by the teacher. Fantastic lesson!
Functions and Everyday Situations
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
Transformation of Functions Exploration
Functions are on the move! This lesson plan provides an opportunity for learners to explore transformations of functions. The activity illustrates the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for both positive and negative values of k. Working in small groups, students complete a table of values for a parent function and an assigned transformation of that function. After sketching both graphs on the same coordinate plane, they analyze their results and write a conjecture about how the value of k affects the original function. Each group shares its findings with the class. The results of the activity are reinforced by using graphing calculators to graph the functions and comparing with the sketches done with pencil and paper. The activity concludes with learners applying what they have learned to write equations for functions when given their graphs.
Quadratic Functions and Graphs
Apply quadratic function graphs to real-life scenarios to develop deeper comprehension through mathematical modeling. This lesson does not provide explicit activities, but rather can be used as a guide. It lists a variety of essential questions, assessment considerations, and instructional strategies that can be adapted to fit the needs of your classroom.
Graphing Absolute Value Functions
The skill set for this lesson is to have learners use tables to generate functions and functions to generate graphs. They work through a series of worksheets with the instructor to determine absolute value, domain, x and y intercept and complete transformations. All of the necessary worksheets and a homework assignment is included.
Building a Quadratic Function
Grab a box of toothpicks and build a model of a dog pen in a lesson that introduces quadratic functions. Students work in groups to investigate how the area of a rectangle with a fixed perimeter varies with different lengths and widths. They record their observations, look for patterns, and build a function to describe the data. Learners make important connections about maximum, minimum, symmetry, and increasing and decreasing intervals when they use a graphing calculator to graph their data points and the corresponding function. Note that the introduction to the lesson task states the dog pen is to be in the shape of a square. The activity is likely to be more productive if the more general term rectangle is used instead. Pupils may question the need to investigate scenarios with different lengths and widths if they are told in the beginning that the pen is to be a square.