Which of the following functions is graphed below?
A. y=|x-2|-3

B. y=|x+2|-3

C. y=|x-2|+3

D. y=|x+2|+3

C: y = |x-2| + 3

Step-by-step explanation:

When dealing with transformations, the numbers in the parentheses is the horizontal translation and the numbers outside the parentheses are vertical translation. The only reason the lines are | rather than ( is because they are absolute value.

When taking the horizontal measures, you always flip the sign. So since it is going to the right 2 times, you would think it would be +2, but since it is in the parentheses it would be -2.

When taking the vertical measures, it's just standard thought. So since it is up 3 it would be +3.

Putting all of that together would give you |x-2|+3

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

i got 10.28 but that rounds up to 10.3