SOLUTION: HELP PLEASE!!!!! THANK YOU I need to take the original functions and define f(x). Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!? 1. y=x^2-2

Algebra ->  Rational-functions -> SOLUTION: HELP PLEASE!!!!! THANK YOU I need to take the original functions and define f(x). Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!? 1. y=x^2-2       Log On


   



Question 90207: HELP PLEASE!!!!! THANK YOU
I need to take the original functions and define f(x). Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!?
1. y=x^2-2 shift down 3 and left 4
2. y=2x=3 shift left 5
3. y=4x-2 shift down 3 and right 2
4. y=-1/2x^2 shift left 4 and widen by 2
Thank you for your help
llo

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

HELP PLEASE!!!!! THANK YOU
I need to take the original functions and define f(x). 
Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!? 
1. y=x%5E2-2 shift down 3 and left 4
2. y=2x=3 shift left 5
3. y=4x-2 shift down 3 and right 2
4. y=-%281%2F2%29x%5E2 shift left 4 and widen by 2 
Thank you for your help
llo


Rules:
1. To shift UP N units, ADD +N TO THE RIGHT SIDE.
2. TO shift DOWN N units, ADD -N TO THE RIGHT SIDE.
3. To shift RIGHT N units, REPLACE x by (x - N) 
4. To shift LEFT N units, REPLACE x by (x + N)
5. To STRETCH by a factor of N > 1, MULTIPLY the RIGHT SIDE by N.
6. To SHRINK by a factor of N < 1, MULTIPLY the RIGHT SIDE by N
7. To SHRINK by a factor of N > 1, MULTIPLY the RIGHT SIDE by 1/N
7. To WIDEN by a factor of N > 1, REPLACE x by x/N
8. To NARROW by a factor of N < 1, REPLACE x by Nx
9. To REFLECT across the x-axis, MULTIPLY the RIGHT SIDE by -1
10. To REFLECT across the y-axis, REPLACE x by -x
11. TO REFLECT across the origin, REFLECT in the y-axis and then REFLECT in the x-axis.


1. y+=+x%5E2+-+2 shift down 3 and left 4

Shifting down 3 requires adding -3 to the right side, so first we have

y+=+x%5E2+-+2+-+3

Simplifying,

y+=+x%5E2+-+5

Shifting left 4 requires replacing x by (x + 4)  so
now we have:

y+=+%28x+%2B+4%29%5E2+-+5

y+=+x%B2+%2B+8x+%2B+16+-+5

y+=+x%B2+%2B+8x+%2B+11

Label it f%28x%29

f%28x%29+=+x%B2+%2B+8x+%2B+11



-------------------------------

2. y=2x=3 shift left 5

You botched that equation, that second = should either be a + or a -,

Either way, to shift left 5, replace x by %28x+%2B+5%29

If it was supposed to be y+=+2x+%2B+3, then when we shift that left 5 we get

y+=+2%28x+%2B+5%29+%2B+3

y+=+2x+%2B+10+%2B+3

y+=+2x+%2B+13

If it was supposed to be y+=+2x+-+3, then when we shift that left 5 we get

y+=+2%28x+%2B+5%29+-+3

y+=+2x+%2B+10+-+3

y+=+2x+%2B+7

Label it f%28x%29

f%28x%29=3x%2B7


----------------------------------------------

3. y+=+4x+-+2 shift down 3 and right 2

To shift down 3 we add -3 to the right side:

y+=+4x+-+2+-+3

y+=+4x+-+5

To shift right 2 we replace x by %28x+-+2%29 in the right side

y+=+4%28x+-+2%29+-+5

y+=+4x+-+8+-+5

y+=+4x+-+13

Label it f(x)

f%28x%29=4x-15 

--------------------------------------

4. y+=+-%281%2F2%29x%5E2 shift left 4 and widen by 2
 
To shift left 4 units we replace x by %28x+%2B+4%29

y+=+-%281%2F2%29%28x+%2B+4%29%5E2

To widen by 2, we replace x by %28x%2F2%29 

y+=+-%281%2F2%29%28x%2F2+%2B+4%29%5E2

y+=+-%281%2F2%29%28x%2F2%2B8%2F2%29%5E2

y+=+-%281%2F2%29%28%28x%2B8%29%2F2%29%5E2

y+=+-%281%2F2%29%28%28x%2B8%29%5E2%2F%282%5E2%29%29

y+=+-%281%2F2%29%28%28x%2B8%29%5E2%2F4%29

y+=+-%281%2F8%29%28x%2B8%29%5E2

y+=+-%281%2F8%29%28x%5E2%2B16x%2B64%29

y+=+-%281%2F8%29x%5E2-2x-8

Label it f%28x%29

f%28x%29+=+-%281%2F8%29x%5E2-2x-8

Edwin