Transformations of Linear Functions For each pair of functions, describe a transformation that maps f(x)to g(x).
1. f(x)=x; g(x)= –x
2. f(x)= x; g(x)= (x–1)+ 7
3. f(x)= x; g(x)= 2(x+ 4)
4. f(x)= x;()= -2/3+4
5. f(x)= x; g(x)= –(x–3)–5
6. f(x)= x;()= 1/2−3

1. lowered one unit

2. raised three units

Step-by-step explanation:

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use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: