Question

Given the parent function

Answer 1

Answer:

B. Translated 5 units to the right and then 2 units downwards

Step-by-step explanation:

We are given that,

The parent function $f(x)=x^2$ is transformed to the function $g(x)=(x-5)^2-2$.

As we know,

Translation shifts the figure in any direction and changes the function f(x) to f(x)±k or f(x±k) depending on the direction.

From the function $g(x)=(x-5)^2-2$, we see that,

The parent function f(x) is changed to f(x-5)-2.

That is, the function f(x) is translated 5 units to the right and then 2 units downwards to obtain the function g(x).

So, option B is correct.

Answer 2

Answer:

The correct option is B. Translated 5 units to the right and then 2 units downwards

Step-by-step explanation:

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. If we look at the comparison of the graphs in the attached figure we can clearly see that the daughter function is translated 5 units to the right and then 2 units downwards.