Day 6 Notes: Reflections and Multiple transformations

The effect of changing: y = x to y = x

1. Complete the first part of the table by graphing y = x . Graph this with a dotted line.

2. Then, complete the table for y = x , and graph with solid line.

3. Write a sentence that describes the transformation:

The effect of changing: y = x to y = x

1. Complete the first part of the table by graphing y = x . Graph this with a dotted line.

2. Then, complete the table for y = x , and graph with solid line.

3. Write a sentence that describes the transformation:

Brain Break: Dance Party!!

x y = x y = x

0

1

4

9

x y = x x y = x

0

1

4

9

Hint: Pick x values here that would

work well for the second function!

Thinking further:

a. What do you think would happen to the graph of y = (-x) 2? See if you are right by getting out your

graphing calculator and graphing y1 = x2 and y2 = (-x)2

b. Identify the parent function, and then describe how it is transformed (either reflecting across the

x- axis or reflecting across the y-axis.

a. y = -x2 b. | | y x c. 3

y x

Part 2: Multiple Transformations

Multiple vertical transformations

1. Shift y = |x| three units up and 2. Reflect y = |x| across the x-axis

then reflect across the x-axis. and then shift three units up.

We get a different result depending on what we do first! Which graph is correct?

3. Describe the transformation of the parent function in each of the following:

a. y = 2x3 – 5 b. y =

19

3x c. y = –x

2 + 4

d. y = 5|x|–1 e. y = –4x2 + 5 f. y =

18

2x

4. Graph y = –x2 + 4 5. Graph y = –5|x| – 1

Let’s practice domain and range for the last two functions:

Domain: Domain:

Range: Range:

(6-8) Write the equation based on the described transformations.

6) Square root function 7) Cubic function reflected 8) Abs. value function

vertically stretched b.a.f.o. 3 over the x-axis and shifted reflected over the x-axis,

and shifted up 8 units down 2 units vertically shrunk b.a.f.o.

¼ and shifted up 6 units