Question

Using Basic Graphs and 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.


Below is a list of the Function Families that you must use. You must use at least 1 for each.

1. y = mx + b slanted line
2. y = c horizontal line
3. x = c vertical line
4. y=|x| absolute value
5. y=x^2 parabola (quadratic)

Requirements:
1. You must use all 5 of the functions listed above.
2. You must have at least 10 different functions used.
3. You must use some sort of transformation on at least 8 of your functions
4. Your picture must be recognizable

**You dont have to draw you can just give me at least 10 functions that uses all the 5 functions that creates a picture that we all know and 8 of the must have some sort of transformation.**

Answer 1

I can help you with your project by providing some examples of functions that can be used to draw a house using basic graphs and transformations. Here are some possible functions:

- y = 2x + 10 (slanted line for the roof)

- y = 10 (horizontal line for the top of the house)

- x = -5 (vertical line for the left side of the house)

- x = 5 (vertical line for the right side of the house)

- y = |x| - 5 (absolute value for the door)

- y = -x^2 + 10 (parabola for the window)

- y = -2 (horizontal line for the bottom of the house)

- y = 2x - 4 (slanted line for the chimney)

- y = 6 (horizontal line for the top of the chimney)

- y = -0.5x + 3 (slanted line for the smoke)

These are just some examples, you can modify them or use different functions to create your own picture. You can also use a tool like Desmos. to graph your functions and see how they look. I hope this helps you with your project.

Answer 2

y = x^2 (parabola) transformed by stretching

y = x + 3 (vertical line) transformed by shifting

y = 3x + 7 (horizontal line) transformed by stretching

y = -x + 8 (slanted line) transformed by reflecting and scaling

y = |x| (absolute value) transformed by shifting

y = x^3 + 3x^2 (cubic polynomial) transformed by compressing

y = x^2 + 1 (quadratic) transformed by reflecting and scaling

y = sqrt(x) (root function) transformed by shifting

y = x + sin(x) (sinusoidal) transformed by rotating

y = 2x + 3 (horizontal line) transformed by compressing and shifting