Question

NO LINKS!!!!!

Part 2: Draw sketches (including several accurate point coordinates) for the following functions. Name all of the transformations.

4. y = -1/3 | x - 2 | - 4

5. y = 1 / ( x + 5) - 3

6. (x - 1)^2 + (y + 2)^2 = 4

Answer 1

see below

Explanation:

We can use the equation

y = -a f(-b (x-h)) +k

The first negative is a reflection about the x axis

a is a horizontal stretch if it is >1 or a compression if less than 1

The negative inside the function is a reflection about the y axis

b is a horizontal compression if >1 or a compression if less than 1

h shifts the function left ( h<0) or right if (h>0)

k shifts the function up if k>0 or down if k <0

4. y = -1/3 | x - 2 | - 4

parent function |x|

reflection about the x axis

1/3 horizontal compression

shift 2 units to the right

4 units down

y = 1 / ( x + 5) - 3

The parent function is 1/x

shift is 5 units to the left and 3 units down

6. (x - 1)^2 + (y + 2)^2 = 4

(x - 1)^2 + (y + 2)^2 = 2^2

This is a circle of radius 2

The center is shifted from the origin 1 unit to the right and 2 units down