For the graph of an exponential function suppose the y-intercept is negative in the common ratio or is greater than one for this graph as X increases y will

Option (1) increase.

Step-by-step explanation:

Let an exponential function is having common ratio = 3 ( greater than 1) and y-intercept = -1

So the function is,  

Now we prepare a table for the values of x and f(x),

x          -1          0        1        2

f(x)      -1.67     -1        1        7

We find from the table that the values of the function are increasing with the increase in the values of x.

Therefore, Option (1) increase will be the answer.

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}