Which function represents a horizontal shift of ƒ(x) = 5(2)^3x by 4 units to the right? a. y = 0 b. y = 3 c. y = 4 d. y = 5

General Idea:

Say if f(x) is the parent function, then f(x-c) represents transformation described as horizontal translation or shift of f(x) by ' c ' units to the right.

Applying the concept:

Here we are given a function , after the transformation of horizontal shift of 4 units to the right, the function will be given as below:

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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.