Question

The graphs below have the same shape. What is the equation of the blue

graph?
G(x) = -
6-
F(x)=x³-5
OA. G(x) = x³ -
2
OB. G(x) = x³ + 2
OC. G(x) = (x-2)³
OD. G(x) = (x + 2)³
G(X) = ?
Please help!

Answer 1

Since the graphs shown above have the same shape, the equation of the blue graph is: C.
`G(x)=(x-2)^3`

In Mathematics and Geometry, the translation of a graph to the right would add a number to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - h)

Conversely, the translation of a graph up would add a number to the numerical value on the y-coordinate of the pre-image:

g(x) = f(x) + k

Based on the information provided, we can logically deduce that the parent function
`f(x)=x^3`, was horizontally shifted to the right by 2 units, in order to produce the following transformed function;

h = 0 + 2

h = 2 units right.

By substituting the value of h, we have;

G(x) = F(x - h)

`G(x)=(x-2)^3`