When a function is translated, the function is shifted or moved by some units to get a new function. The function g(x) after translating f(x) 6 units up is: [tex]g(x) = 2x -3[/tex]
Given that
[tex]f(x) = 2x -9[/tex]
The rule of translating 6 units up is:
[tex](x,y) \to (x,y+6)[/tex]
So, we have:
[tex]g(x) = f(x) + 6[/tex]
Substitute [tex]f(x) = 2x -9[/tex]
[tex]g(x) = 2x - 9 + 6[/tex]
[tex]g(x) = 2x -3[/tex]
Hence, the function g(x) after translating f(x) 6 units up is:
[tex]g(x) = 2x -3[/tex]
Read more about translations at:
https://brainly.com/question/12463306
