Tia states that the graph of g(x) = (x – 2)3 + 7 is a translation of 2 units to the left and 7 units up from f(x) = x 3. is tia’s description of the translations correct? explain.

No, Tia's description is not correct.

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

If , the function is shifted up "k" units.

If , the function is shifted down "k" units.

If , the function is shifted left "k" units.

If , the function is shifted right "k" units.

Knowing this, and given the function g(x):

And the parent function:

 You can identify that the graph of the function g(x) is a translation of 2 units to the right and 7 units up from the parent function f(x).

Therefore, Tia's description is not correct.

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.

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step-by-step explanation: