Algebra and Trigonometry: Functions

Here, we’ll have a discussion and a general overview of the concept of functions to build a foundation upon which we can build the rest of the course.

Here, we’ll have a discussion and a general overview of the concept of functions to build a foundation upon which we can build the rest of the course.

Here, we’ll have a typical coffee shop menu and based on that decide whether price is a function of item and vice versa.

Here, we’ll solve two examples, first a typical average grade system and second a list of famous baseball players of all time. In each case, we decide whether one set can be considered a function of the other one and vice versa.

In this video, we’ll talk about function notation like f(x). We learn how and in what situations we can use that and what is basically represented by it. Moreover, we’ll do some examples to learn the concept better.

In this video, we’ll study some relationships between pairs of numbers represented in form of tables. Each table has a set of inputs and outputs. After studying each table, we decide whether the table represents a function or not.

In this video, you’ll learn how to evaluate functions at different points for inputs. We’ll also learn what the inverse of this situation would look like. Moreover, we’ll go through some example to solidify the concepts learned here.

In this video, you’ll learn how to figure out the input values in a function that created a specific output.

In this video, you’ll learn how to determine whether a variable in a formula is a function of the other variable. For example, in the formula x² + y² = 1, you can determine whether y is a function of x or not.

In this video, you’ll learn how to evaluate function values by reading the information related to the function represented in a tabular form. Each input in the table corresponds to an output and so based on that, you can evaluate any desired input.

In this video, you’ll learn how to use the graph of a function in order to determine the output value related to any input value present in the domain of the function. For example, by looking at the graph of a function, you can identify which output is related to the input x =4 and based on that you can write, f(4) = “that identified output value read on the graph”. You can also do this to solve equations like f(x) = 2, in which you could identify for which value/values of x, you would have an output value of 2.

In this video, you’ll learn how to determine whether a function is one-to-one, meaning that each output value corresponds exactly to one input value and that there are no repeated x or y values. We’ll also do some exercises to understand the concept better.

In this video, you’ll learn how you can use a vertical line, run it through the domain of a function parallel to the y axis to decide whether a graph represent a function or not.

In this video, you’ll learn how you can use a horizontal line, run it through the range of a function, parallel to the x axis, to decide whether a function is one-to-one or not.

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

In this video, we’ll give you a summery of the interval notation. For example, x > a on a number line in interval notation as (a, infinity). We’ll also do a few examples finding the domains of a few functions.

In this video, you’ll learn how to find the domain of a function. We’ll also do a few exercises to learn the concept properly.

In this video, you’ll learn how to find the domain of a function. We’ll also do a few exercises to learn the concept properly.

In this video, you’ll learn how to use inequality notation, set-builder notation and the interval notation to specify domain and range of a function.

In this video, you’ll learn how to describe sets on a real-number line in set-builder, inequality and interval notations.

In this video, you’ll learn how to find the domain and range of functions based on the graph of the function. We’ll also do some examples to learn the concept better.

In this video, we’ll study the domains and ranges of some famous toolkit functions.

In this video, we’ll find the domain and range of square root functions.

In this video, you’ll learn what piecewise-defined functions are and in what sort of situations they can be used.

p190, e12 - In this video, you’ll learn how to interpret and graph a piecewise function that represents how a cell phone company charges their customers for data transfer.

p191, e13 - In this video, we’ll draw the graph of a piecewise functions that consists of a three pieces.

In this video, we’ll introduce the concept of rate of change. We’ll use an example of the average cost of a gallon of gasoline in dollars over the period of 7 years from 2005 to 2012 and study the change in cost over different periods between the two years.

In this video, we'll learn the practical meaning of average rate of change using a practical example.

In this video, we'll go through two interesting examples of calculating the average rate of change.

In this video, we're going to analyze the graph of a function and identify in what intervals the function is increasing or decreasing.

In this video, we're moving the toolkit reciprocal function to the right and up. We'll then find the formula of the transformed function, draw the graph of both functions and compare them.

In this video, we're developing a function that represents a learning model. The function is a transformation of one of the toolkit functions. Three steps of transformation are applied to the function. 

In this video, we're going to graph the vertical and horizontal transformations of the toolkit function f(x) = x^2

In this video, we have a function in the form of a polynomial of degree 4. We'll verify whether the polynomial is even or odd. 

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p237 - In this video, we're taking the identity toolkit function, f(x) = x and stretch the function and move it down as well. We'll create a formula for the new function and draw the graph as well. 

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p238 - In this video, we'll create a new function based on a population of fruit flies. The new function created based on the original function progresses through its life span twice as fast as the original function and so it represents a horizontal compression. 

p238 - In this video, we'll create a new function based on a population of fruit flies. The new function created based on the original function progresses through its life span twice as fast as the original function and so it represents a horizontal compression. This is the same problem as the last video. It has been solved in a different way. 

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p239, ti11 - In this video, we take the toolkit square root function and stretch it by a factor of 3. We then find the formula of the stretched function. 

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