Question

The function f(x) = square root of x is translated left 5 units and up 3 units to create the function g(x)

Answer 1

Answer:

The domain of g(x) is {xI x > -5} ⇒ first answer

Step-by-step explanation:

* Lets talk about the transformation at first

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* lets revise the meaning of the domain

- The domain is all values of x that make the function defined

- Find the values of x which make the function undefined

- The domain will be all the real numbers except those values

* Now we can solve the problem

∵ f(x) = √x

- f(x) translated 5 units to the left, then add x by 5

∴ f(x) ⇒ f(x + 5)

- f(x) translated 3 units up, then add f(x) by 3

∴ f(x) ⇒ f(x) + 3

- The function g(x) is created after the transformation

∴ g(x) = f(x + 5) + 3

∵ f(x) = √x

∴ g(x) = √(x + 5) + 3

- The function will be defined if the value under the square root

  is positive (means greater than 0)

∵ The expression under the square root is x + 5

∴ x + 5 > 0 ⇒ subtract 5 from both sides

∴ x > -5

- The domain will be all the real numbers greater than -5

∴ The domain of g(x) is {xI x > -5}