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The function f(x) = x 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 + 712 - 3
g(x) = (x - 3)2 - 7
g(x) = (x-3)2 + 7
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User Bluss
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Answer:

Second option:
g(x)=(x+7)-3

Explanation:

The exercise is actually:

"The function
f(x) = x^2 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 "

Below are shown some transformations for a function f(x):

1. If
f(x)+k, the function is shifted up "k" units.

2. If
f(x)-k, the function is shifted down "k" units.

3. If
f(x+k), the function is shifted left "k" units.

4. If
f(x-k), the function is shifted right "k" units.

In this case the exercise provides you the following parent function:


f(x) = x^2

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:


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

Therefore, you can determine that the function g(x) is:


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

User DiaMaBo
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