State the order and type of each transformation of the graph of the function f(x)=1/2[(x+2)^2-9] as compared to the graph of the base function left 2 units, vertical compression by a factor of 0.5, down 9 units

left 2 units, horizontal stretch by a factor of 2, down 9 units

left 2 units, down 9 units, vertical compression by a factor of 0.5

left 2 units, down 9 units, horizontal stretch by a factor of 2

C) left 2 units, down 9 units, vertical compression by a factor of 0.5.

Step-by-step explanation:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis and if there is a vertical stretch.

Parent Function:  

g ( x ) = x 2

Horizontal Shift: Left  2  Units

Down: 9 Units

Vertical Shift: Down  0.5  Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: Compressed

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.