What effect does changing the function f(x)=2sin(x/2)−1 to the function g(x)=2sin(x)−5 have on the graph of f(x)?

See the step by step for explanation and answer

Step-by-step explanation:

The first function is a sin function with an amplitude of 2, and a period of 4pi.  The -1 moves it down from its original position 1 unit.  There is no phase shift here.  The normal period of a sin function is 2pi, which means that one revoution of the graph (one Up-down-up to put it in simplest terms) starts at 0 and ends at 2pi.  The x/2 means that the value to consider for the period change is 1/2.  The formula to solve for a period change is 2pi/that value (most books call it b).  So we have 2pi/(1/2), which algebraically solves to 4pi.  That means that one up-down-up of the function starts at 0 and ends at 4pi.

That second function doesn't have a b value, so its period is still 2pi.  The -5, however, moves the whole graph down 5 units from the original position (which is 4 units below the first graph).  The second function also has an amplitude of 2. I hope this helps a bit!

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.