Day 6 Notes: Reflections and Multiple transformations
Transcript of Day 6 Notes: Reflections and Multiple transformations
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