Question

The graph of the function ƒ(x) = 4√x is shifted down by three units. What is the domain of the resulting function?

Answer 1

Answer:

The domain of the transformed function is:

[0,∞)

Step-by-step explanation:

We know that the domain of  a function is the set of all possible values where the function is defined i.e. the possible x-values.

Now we are given a parent function f(x) as:

$f(x)=4\sqrt{x}$

Now, it is given that the function f(x) is transformed three units downward.

So, the resulting function g(x) is given as:

$g(x)=4\sqrt{x}-3$

Hence, the function g(x) is defined for all x≥0.

( Since, the square root function is not defined for negative real numbers and for rest values it is defined)

Hence, the domain is given as:

[0,∞)