Question

What is the range of the function f(x) = (x + 3)2 + 4?

Answer 1

Range of $f(x)=(x + 3)^2 + 4$ is [4,∞).

Step-by-step explanation:

Here we have , function $f(x)=(x + 3)^2 + 4$  , We need to find range of this function . Let's find out:

In the function $f(x)=(x + 3)^2 + 4$ , Let's focus on $(x+3)^2$ : It's a perfect square whose value will be always positive and greater then equal to zero i.e.

⇒ $(x+3)^2\geq 0$ , So minimum value of $(x+3)^2$ is 0 at x=-3 . ∴

⇒ $f(x)=(x + 3)^2 + 4$

⇒ $f(-3)=(-3+ 3)^2 + 4$

⇒ $f(-3)= 4$

Minimum value of $f(x)=(x + 3)^2 + 4$ is 4 , And maximum value of $f(x)=(x + 3)^2 + 4$  can be ∞ as value of x can be increased . Therefore , Range of $f(x)=(x + 3)^2 + 4$ is [4,∞).