The graph shows the function f(x) which equation represents f(x)

The correct option is 3.

Step-by-step explanation:

The parent cube root function is

From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.

If the parent cube root function is reflected across the y-axis, then x is replaced by -x.

Now, the graph of new function sifts 1 unit down. So, the required function is

The graph shows the function .

From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).

Check the above function by these points.

At x=-8,

At x=0,

At x=8,

All these points satisfy by the abobe function. It means the above function is correct.

Therefore the correct option is 3.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.