Question

NO LINKS!! Please help me with this translation: 2 units right and 5 units up​

Answer 1

g(x) = 5|(x - 2) - 2| - 2

Explanation:

To shift 5 units right :

⇒ f(x) = 5|(x - 2) - 2| - 7

⇒ Applied rule : a units right → f(x) = (x - a)

To shift 5 units up :

⇒ g(x) = 5|(x - 2) - 2| - 7 + 5

⇒ g(x) = 5|(x - 2) - 2| - 2

Answer 2

`g(x)=5|x-4|-2`

Explanation:

Translations

For
`a > 0`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

Parent function:

`f(x)=5|x-2|-7`

Translate 2 units right:

`\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}`

Then translate 5 units up:

`\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}`

Therefore:

`\implies g(x)=5|x-4|-2`