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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|

Respuesta :

rgwoot
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|
Ver imagen rgwoot

Answer:

C. [tex]f(x)=-4|x|-3[/tex].

Step-by-step explanation:

We have been given a  function formula [tex]f(x)=-4|x|[/tex]. 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.

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex],

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex],

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex],

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex].

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 [tex]f(x)=-4|x|-3[/tex] and option C is the correct choice.

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