Which table represents a direct variation? table a table b table c table d

The table that represents a direct variation is:

                               Table B.

We know that a table is of direct variation if for each x and y there exist a constant k such that:

Now in Table A:

We calculate the ratio of each y and x values as follows:

As we see that we did  not get a constant k from each of the ratios.

Hence, Table A is not a table of direct variation.

Table B:

We calculate the ratio of each y and x values as follows:

As we see that we get a constant k from each of the ratios.

Hence, Table B is  a table of direct variation.

Table C:

We calculate the ratio of each y and x values as follows:

As we see that we did  not get a constant k from each of the ratios.

Hence, Table C is not a table of direct variation.

Table D:

We calculate the ratio of each y and x values as follows:

As we see that we did  not get a constant k from each of the ratios.

Hence, Table D is not a table of direct variation.

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4