Question

What is the equation of the translated function, g(x), if

f(x) = x2?

g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x – 2)2 + 5
g(x) = (x – 5)2 + 2

Answer 1

In all the options g(x) is translation of f(x)

Explanation:

Translation of a function means it shifting either left or right.

or we can say change in variable x .

f(x) =
`a(x-h)^2+k` gives translated by h unit to the right or left according to positive or negative sign of h respectively.

Here in option 1 ,on comparing we have h =-5 therefore its translated by 5 units to the left

in Option 2 : ,on comparing it is h =-2 therefore translated to 2 unit to the left

In option 3 : , on comparing we have h =2 therefore translated to 2 units to the right.

In option 4 : ,on comparing we have h =5 therefore translated to 5 units to the right.

therefore in all the options f(x) is translated.

Answer 2

Translation of a function is moving of the function without changing the shape of the function and without any rotation. So, translating of function means moving its graph left or right in the dierction of the x or y-axes. The function is f(x)=x^2. All of given options are translation of this function,.