Select the correct answer.The function f(x) is given by the table of values.

x 1 2 3 4
f(x) 1 8 27 64
If f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?


x 5 6 7 8
g(x) 5 12 31 68


x 1 2 3 4
g(x) 5 12 31 68


x 5 6 7 8
g(x) 1 8 27 64


x 1 2 3 4
g(x) 4 32 108 256

The solution is Option B.

x = { 1 , 2 , 3 , 4 }

g(x) = { 5 , 12 , 31 , 68 }

The function g ( x ) = x³ + 4

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

when x = 1

f ( x ) = 1

when x = 2

f ( x ) = 8

when x = 3

f ( x ) = 27

when x = 4

f ( x ) = 64

So , the equation will be y = x³   be equation (1)

Now , f(x) is shifted 4 units up to obtain g(x)

So , Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

when x = 1

g ( x ) = 1 + 4 = 5

when x = 2

g ( x ) = 8 + 4 = 12

when x = 3

g ( x ) = 27 + 4 = 31

when x = 4

g ( x ) = 64 + 4 = 68

Therefore , the function is g ( x ) = x³ + 4

Hence , the function is g ( x ) = x³ + 4

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Answer:

The second answer is correct.

Step-by-step explanation:

So g(x) = f(x) + 4

If f(x) = 1, 8, 27, and 64 then g(x) = 5, 12, 31, and 68.