Objective: To identify the basic functions of formulas and graphs. To sketch the

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Objective:
To identify the basic functions of formulas and graphs.
To sketch the shift, reflection, compress, stretch, and inverse transformations of a function using demos.com
To describe features of each family of curves for each function
Introduction:
The concept of a function is a building block of many concepts of modern mathematics. It is as important in modern mathematics development as integers in arithmetic computation. We will see that many other complicated functions can be obtained through the compositions or combinations of those basic functions. Hence it is crucial to know those basic functions well. In this project, you will learn the properties of the basic functions in algebraic, graphic, and descriptive methods.
List of functions to be studied in your function library
Square Function f(x)=x2(−∞,∞)
Square Root Function f(x)=xx≥0
Absolute Function f(x)=|x|(−∞,∞)
Exponential Function f(x)=2x(−∞,∞)
Logarithmic Function f(x)=log2⁡(x)(0,−∞)
Reciprocal Function f(x)=1x(−∞,0)U(0,∞)
x is the input of a function and f(x)is the output of a function?
Submission requirement for each of the six functions.
You will submit a document including the following:
A set of graphs of each function and all possible transformations labeled with the formula of each curve.
A list of formulas and domains and ranges for each curve
A summary of special characters or features of this family of functions.
Suggested procedures for creating graphs and transformations
Step 1. Graph a function and all its possible transformations on desmos.com.
Step 2. Export your graph (Use this link to get help for Export graphs on desmos.com)
Video recording of activity for graphs of square root function and its transformation using desmos.com (https://www.3cmediasolutions.org/privid/304665?key=c68972a8aab5884a2f06d79f08eaf25af46c96ca)
Step 3. Import your graph to a word document
Step 4. Set the graph to the desired size and label each curve.
A sample submission of cubic function (not in the list of the function library——see file no.1
Formulas of each function, its domain and range—–see file no.2
Descriptive Summary of this family of function
This function is a one-to-one function. The curve either increases or decreases. The domain and range are always (−∞,∞).
This function is a one-to-one function whose graph passed both horizontal and vertical line tests.
This family of the curve has common features and it starts from one corner of either upper left or lower left and continues either upwards (increasing) or downwards (decreasing) to the opposite half of the plan to infinity. No maximum point or the minimum point within the domain.
The vertical reflection and horizontal reflection are identical because this function is symmetric with respect to the center of the coordinate.
The special points are (0,0), (1,1), and (−1,−1)

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