Question

Which function represents the graph of f(x)=−4|x| after it is translated 3 units down?

A. g(x)=-4|x+3|
B. g(x)=-4|x|+3
C. g(x)=-4|x|-3
D. g(x)=-4|x-3|

Answer 1

Which function represents the graph of f(x)=−4|x| after it is translated 3 units down?

A. g(x)=-4|x+3|
B. g(x)=-4|x|+3
☆☆☆☆☆☆☆☆☆☆☆C. g(x)=-4|x|-3
D. g(x)=-4|x-3|

Answer 2

C.
`f(x)=-4|x|-3`.

Explanation:

We have been given a function formula
`f(x)=-4|x|`. We are asked to find the function that is obtained from translating our given function by 3 units down.

We will use transformation rules to solve our given problem.

`f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}`,

`f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}`,

`f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}`,

`f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}`.

Since we need to translate our given graph by 3 units down, so we need to subtract 3 outside of our given function.

Therefore, our required graph would be
`f(x)=-4|x|-3` and option C is the correct choice.