Respuesta :
Answer:
Second option: [tex]g(x)=(x+7)-3[/tex]
Step-by-step explanation:
The exercise is actually:
"The function [tex]f(x) = x^2[/tex] is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?
[tex]g(x) = (x-7)^2 - 3\\g(x) = (x + 7^2 - 3\\g(x) = (x - 3)^2 - 7\\g(x) = (x-3)2 + 7[/tex] "
Below are shown some transformations for a function f(x):
1. If [tex]f(x)+k[/tex], the function is shifted up "k" units.
2. If [tex]f(x)-k[/tex], the function is shifted down "k" units.
3. If [tex]f(x+k)[/tex], the function is shifted left "k" units.
4. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
In this case the exercise provides you the following parent function:
[tex]f(x) = x^2[/tex]
Then, keeping on mind the transformations explained before, if the given function f(x) is translated 7 units to the left and 3 units down in order to form the function g(x), then you can conclude that:
[tex]g(x)=f(x+7)^2-3[/tex]
Therefore, you can determine that the function g(x) is:
[tex]g(x)=(x+7)^2-3[/tex]