Determine whether the function is a linear transformation. t: p2 → p2, t(a0 + a1x + a2x2) = (a0 + a1 + a2) + (a1 + a2)x + a2x2.

Answer with Step-by-step explanation:

We are given that a function

We have to determine the given function is a linear transformation.

If a function is linear transformation then it satisfied following properties

2.

Hence, the function is a linear transformation because it satisfied both properties of linear transformation.

d is the answer

step-by-step explanation:

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.