Create two tables with at least four coordinates each. In the first table, choose coordinates that make the relation a function. In the second table, choose coordinates that don't make the relation a function. Explain in complete sentences how you determined which coordinates would define a function and which coordinates would not.

9514 1404 393

Step-by-step explanation:

A relation that is a function has unique x-values. A relation that is not a function has at least one x-value that is repeated. The y-values do not need to be unique in either case, except that a repeat of the same (x, y) pair does not disqualify a relation from being a function.

In the table shown above, the non-function has the x-value of 3 repeated with different y-values.

its a little blurry tbh

step-by-step explanation:

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}