Using Basic Graphs and Transformations to Draw Pictures



Using Basic Graphs & Transformations to Draw Pictures

The purpose of this project is for you to draw a picture that incorporates many of the “basic graphs” that we have studied in class as well as your knowledge of transformations (vertical shifts, horizontal shifts and stretches). You will create equations that, when graphed, will create your picture.

Here is a list of the Function Families that you can/must use:

1. y = mx + b linear, slanted line

2. y = c horizontal line

3. x = c vertical line

4. y = | x | absolute value

5. y = x2 parabola (quadratic)

6. y = x3 cubic

7. y = [pic] square root (radical)

Requirements:

1. 3 different “Function Families” make you eligible for a ‘C’

2. 5 different “Function Families” make you eligible for a ‘B’

3. 7 different “Function Families” make you eligible for an ‘A’

4. You must use at least 20 different functions.

5. You must use some sort of transformation on at least 15 of your functions.

6. You must include the domain of each function you graph.

7. Your picture must be recognizable.

8. Bonus points can also be earned for extra creative drawings as perceived by the teacher.

What You Will Turn In When Finished:

1. A “hand drawn” sketch of your picture with each graphed function labeled with the number

of the function it is on your list (see number 2 below).

2. A list of all the functions you used in your drawing numbered so that I can find

that graph on your picture.

For example: 1.) y = 2x + 3

2.) y = (3x+2)2 - 2

3.) x = -2

4.) y = | x – 2 | + 3

And so forth.

3. A final draft of your picture with each function labeled. Color your picture! This can be done by hand or on a computer using desmos.

Due Date:

Graph Name __________________________________

[pic]

Functions List Name __________________________________

|Number on graph |Equation |Function Family |Transformations |Domain Used |

| | | | |(Use Interval Notation) |

|EX |y = (x+2)2 - 2 |parabola (quadratic) |Vertical translation 2 units down |-3≤x≥5 |

| | | |Horizontal translation 2 units left | |

|1 | | | | |

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