Question

*If I have anything wrong, please let me know, so I can learn from my mistake.*

Part 1: Describe the change to the parent function (cubed root).
Part 2: Create an equation based on the following transformations.

*My Answer will be in a PDF File to be checked/graded.*

Answer 1

@campbell_st

Answer 2

okay

Answer 3

the rest looks good.

Answer 4

so if it's f(x) = -4x^2 it's reflected over the y - axis

Answer 5

Pardon me. I think I have made some mistakes here. I had it clearly in my mind and mistyped x and y.

f(x) transformed to -f(x) is reflection over the x-axis
f(x) transformed to f(-x) is reflection over the y-axis.

Answer 6

could I write number 17. f(x) = -1/4 (x - 6)^3 + 2

Answer 7

All of your answers looks correct (including #6 and #7).

Answer 8

Oh, I have not seen the second page yet. All of your answers on page 1 looks correct.

Answer 9

#10 is part of #'s 1-9

Answer 10

#17) p(x) = x^3 (parent function)
f(x) = - (1/4x - 6)^3 + 2 = -{ 1/4( x - 24) }^3 + 2 = -1/64 * (x - 24)^3 + 2
Shift right by 24 units, compress vertically by a factor of 64, reflect about the x-axis, shift vertically up by a factor of 2.

Answer 11

does it have to be like: f(x) = - (1/4x -6)^3 + 2 or can it be -1/4(x - 6)^3 + 2

Answer 12

The function that is given to you is f(x) = - (1/4x -6)^3 + 2
and NOT f(x) = -1/4(x - 6)^3 + 2.

In transformations, if x is replaced by (x-a) we know that is a shift to the RIGHT by 'a' units. Here, we have a factor of 1/4 before x and so we can't say x is being replaced by (x-6). So we have to factor out the 1/4 which is what I did in my previous reply.

Answer 13

read the transformations on the left side of the semicolon

Answer 14

Oh, they are giving you the transformations and asking you for the function?
I was doing problem 17 like problems 1-10 where f(x) is given and you have to describe the transformations. Let me do it the other way and check your answer.

Answer 15

#17) Parent cubic function: x^3
Horizontal *compression* by a factor of 4: x^3 becomes (4x)^3.
Reflection over x-axis: x becomes -x and so (4x)^3 becomes (-4x)^3.
Shift right by 6 units: Replace x by (x - 6). So {-4(x-6)}^3.
Shift up by 2 units: Add +2. So {-4(x-6)}^3 + 2.

Answer 16

so f(x) = -4 (x - 6)^3 + 2

Answer 17

oops, reflection over *x axis*: stick a negative sign in front of the function:
(4x)^3 becomes -(4x)^3.
Shift right by 6 units: Replace x by (x - 6). So -{4(x-6)}^3.
Shift up by 2 units: Add +2. So -{4(x-6)}^3 + 2.

In your previous reply the 4 should be included in the cubing.

Answer 18

So the transformed function is: -{4(x-6)}^3 + 2 = -64(x-6)^3 + 2.

Answer 19

http://www.regentsprep.org/regents/math/algtrig/ATP9/funclesson1.htm

Answer 20

so f(x) = - (4x - 6)^3 + 2

Answer 21

Not quite. The x is replaced by (x-6) and so -(4x)^3 becomes -{ 4(x - 6) }^3.
And then add 2.

Answer 22

f(x) = -(4x - 24)^3 + 2 or f(x) = -64(x-6)^3 + 2

Answer 23

do I really need to simplify it?

Answer 24

It depends on what they are expecting. But to easily describe the transformations it would be better to leave it unsimplified at: f(x) = -{4(x-6)}^3 + 2.

Answer 25

I just want the unsimplified answer that I give

Answer 26

I am using curly brackets to indicate that 4 is getting cubed too.

Answer 27

I appreciate that but it does get confusing when you use too many brackets, so do what I do, because we know the 4 will get cubed

Answer 28

What is your answer? The one in the pdf file has 1/4 and so that is not correct.

Answer 29

the ony I typed in the comments: f(x) = - (4x - 6)^3 + 2

Answer 30

But the above function does NOT have a horizontal shift of 6.
To have a horizontal shift of +6, x should be replaced by (x-6). But in your answer 4x is being replaced by 4x - 6 instead of 4(x-6).

Answer 31

p(x) = -(4x)^3 + 2
f(x) = -(4x - 6)^3 + 2
f(x) is p(x) shifted to the right by 1.5 units and NOT 6 units because
f(x) = -(4x - 6)^3 + 2 = -{ 4(x - 1.5) }^3 + 2.
x in p(x) is being replaced by (x-1.5) and so it is a shift to the right by 1.5 units.
But
f(x) = -(4x - 24)^3 + 2 is p(x) shifted right by 6 units because
f(x) = -(4x - 24)^3 + 2 = -{ 4(x - 6) }^3 + 2 where x in p(x) is being replaced by (x - 6).

Answer 32

we don't use brackets for this we use the setup that I used: For example,
f(x) = 3(x + 4)^3 - 6

Answer 33

The final answer is:
f(x) = -{4(x-6)}^3 + 2
If you don't like the curly brackets, then it is:
f(x) = -(4x - 24)^3 + 2. Not your answer of f(x) = - (4x - 6)^3 + 2

Answer 34

f(x) = -(4x - 24)^3 + 2 is shift to the right by 6 units.
f(x) = -(4x - 6)^3 + 2 is shift to the right by 1.5 units.

Answer 35

did you multiply 4 * 6 to get 24

Answer 36

yes.

Answer 37

I just assumed that if I put (4x - 6)^3 that it shifted to the right 6 units

Answer 38

For positive 'a', f(x-a) shifts f(x) to the right by 'a' units.
If a = 6, then f(x-6) shifts f(x) to the right by 6 units.
If f(x) = x^2, then the right shifted function by 6 units is: f(x-6) = (x-6)^2
But if f(x) = 2x^2, then the right shifted function is f(x-6) = 2(x-6)^2 and NOT
2x^2 - 6.

Answer 39

So if we start with the function f(x) = (4x)^3
and shift it to the right by 6 units it will become { 4(x-6) }^3 = (4x - 24)^3 and
NOT 4x^3 - 6.

Answer 40

I don't like brackets okay

Answer 41

I started with the brackets to show you the steps involved but simplified it later, eliminating the brackets.

Answer 42

For example, f(x) = (5x)^3.
Shift the function to the right by 2 units.
What will be the transformed function?

Answer 43

I think I am clear on what #17 is talking about, so what about the 11 - 16

Answer 44

#11: Since the parent is a cube root function, you need to insert a small 3 before the radical sign to indicate cube root.

Answer 45

is that all for #11

Answer 46

yes.

Answer 47

For #12, you can factor out -1 out of the squaring which will make it +1 so it becomes
(x+2)^2 - 3. But it is up to you if you want to simplify. It all depends on what your teacher is expecting. Both answers are correct.

Answer 48

#13 should be \(\large -\sqrt{x+2}\)

Answer 49

#14) Parent f(x) = x^3
vertical stretch by a factor of 3: 3f(x) = 3x^3
left by 4: 3(x+4)^3
down 6: 3(x + 4)^3 - 6

Answer 50

#15 is correct.

Answer 51

Is 16 reflected over x or the y axis?

Answer 52

x-axis

Answer 53

#16)

\(\Large -\frac 13\sqrt[3]{x+1}\)

Answer 54

- 5 my bad

Answer 55

#16

\(\Large -\frac 13\sqrt[3]{x+1} - 5 \)

Answer 56

So what is the answer to my sample question earlier?

Answer 57

f(x) = (5x)^3. Shift the function to the right by 2 units. What will be the transformed function?

Answer 58

17.) f(x) = - (4x - 24)^3 + 2

Answer 59

yes, 17 is correct. How about the question above?

Answer 60

To shift a function to the right by 2 units, simply replace f(x) with f(x-2).
Here f(x) = (5x)^3
f(x-2) = { 5(x-2) }^3 = (5x - 10)^3 and NOT (5x)^3 - 2.

Answer 61

gtg.

Answer 62

thank you for the help, so are all of my answers checked and okayed

Answer 63

As far as I can tell they all seem okay except for a few corrections here and there. But a double check is always recommended to catch any silly mistakes.

Answer 64

To shift a function to the right by 2 units, simply replace f(x) with f(x-2).
Here f(x) = (5x)^3
f(x-2) = { 5(x-2) }^3 = (5x - 10)^3 and
NOT (5x)^3 - 2 and
NOT (5x - 2)^3.