We were given the answers for these problems. I am looking for an explanation of

Question

We were given the answers for these problems. I am looking for an explanation of the answers and the work proving these answers.

1. For question one, why is the shrink 1/6?

2. For question two, why is the stretch 2?

3. How to determine stretch

4. How to determine stretch

V(-3,-) )-| Transformation:-5 -13 Shrink f@s 3-12 8(x3-12+2 For fx): y-intercept ala35 end behavior. Ass+ ,f(x)+9 3x-12 + 2 v Stretch bo 2)10 24udova Xardy g(x)- Transformation: For f(x): Domain: Range: y 20 x-intercept y4tercept Q-2,4-end behavior. Asxf(x) Ass+_f(x)0-

Explanation / Answer

f(x) = 3sqrt(2(x+3)) - 1
which can be written by taking the 3 back inside the sqrt as

f(x) = sqrt(2*3^2 * (x+3)) - 1

f(x) = sqrt(18(x + 3))- 1

g(x) = sqrt(3(x - 12)) +2

Notice that 18 becomes 3
Thus, a shrink by a factor of 3/18 ---> 1/6

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

f(x) = -sqrt(6 - x)

g(x) = 2/3 * sqrt(3(x - 4)) + 2

g(x) = sqrt(4/9 * 3 * (x-4)) + 2

= sqrt(4/3(x - 4)) + 2

= 2sqrt(1/3*(x-4)) + 2

Because of the 2 multiplied upfrontm,
this can be viewed as a vertical stretch by a factor of 2

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