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.
shift down 3 and left 4
2.
shift left 5
3.
shift down 3 and right 2
4.
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.
shift down 3 and left 4
Shifting down 3 requires adding -3 to the right side, so first we have
Simplifying,
Shifting left 4 requires replacing x by (x + 4) so
now we have:
Label it
-------------------------------
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
by
If it was supposed to be
, then when we shift that left 5 we get
If it was supposed to be
, then when we shift that left 5 we get
Label it
----------------------------------------------
3.
shift down 3 and right 2
To shift down 3 we add -3 to the right side:
To shift right 2 we replace
by
in the right side
Label it f(x)
--------------------------------------
4.
shift left 4 and widen by 2
To shift left 4 units we replace
by
To widen by 2, we replace x by
Label it
Edwin