Question 90207
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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=-(1/2)x^2}}} 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^2 - 2}}} shift down 3 and left 4

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

{{{y = x^2 - 2 - 3}}}

Simplifying,

{{{y = x^2 - 5}}}

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

{{{y = (x + 4)^2 - 5}}}

{{{y = x² + 8x + 16 - 5}}}

{{{y = x² + 8x + 11}}}

Label it {{{f(x)}}}

{{{f(x) = x² + 8x + 11}}}



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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 {{{(x + 5)}}}

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

{{{y = 2(x + 5) + 3}}}

{{{y = 2x + 10 + 3}}}

{{{y = 2x + 13}}}

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

{{{y = 2(x + 5) - 3}}}

{{{y = 2x + 10 - 3}}}

{{{y = 2x + 7}}}

Label it {{{f(x)}}}

{{{f(x)=3x+7}}}


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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 {{{(x - 2)}}} in the right side

{{{y = 4(x - 2) - 5}}}

{{{y = 4x - 8 - 5}}}

{{{y = 4x - 13}}}

Label it f(x)

{{{f(x)=4x-15}}} 

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4. {{{y = -(1/2)x^2}}} shift left 4 and widen by 2
 
To shift left 4 units we replace {{{x}}} by {{{(x + 4)}}}

{{{y = -(1/2)(x + 4)^2}}}

To widen by 2, we replace x by {{{(x/2)}}} 

{{{y = -(1/2)(x/2 + 4)^2}}}

{{{y = -(1/2)(x/2+8/2)^2}}}

{{{y = -(1/2)((x+8)/2)^2}}}

{{{y = -(1/2)((x+8)^2/(2^2))}}}

{{{y = -(1/2)((x+8)^2/4)}}}

{{{y = -(1/8)(x+8)^2}}}

{{{y = -(1/8)(x^2+16x+64)}}}

{{{y = -(1/8)x^2-2x-8}}}

Label it {{{f(x)}}}

{{{f(x) = -(1/8)x^2-2x-8}}}

Edwin</pre>