Question

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). which represents g(x)? g(x) = (x − 7)2 − 3 g(x) = (x 7)2 − 3 g(x) = (x − 3)2 − 7 g(x) = (x − 3)2 7

Answer 1

Translated left means to add to your x
Translated down means to subtract from your rule
so...
`g(x)=(x+7)^2-3`

Answer 2

Option (2) is correct.

The function
`g(x)=(x+7)^2-3` is obtained by translating
`f\left(x\right)=x^2` 7 units to the left and 3 units down.

Explanation:

Given : parent function
`f\left(x\right)=x^2`

We have find the function g(x) such that
`f\left(x\right)=x^2` is translated 7 units to the left and 3 units down to form the function g(x)

Translation of a function is a process of shifting the parent function.

When we add or subtract anything in the brackets of parent graph, the graph will move horizontally and when we add or subtract anything outside the brackets of parent graph,the graph will move vertically.

Now when
`f\left(x\right)=x^2` is translated 7 units to the left that is we are adding 7 in the brackets of parent graph
`f\left(x\right)=x^2`

We get

`=(x+7)^2`

Now, the graph obtained has been translated 3 units down that is we are subtracting 3 outside the brackets of graph that is

`g(x)=(x+7)^2-3`

Thus, the function
`g(x)=(x+7)^2-3` is obtained by translating
`f\left(x\right)=x^2` 7 units to the left and 3 units down.

Option (2) is correct.