Step by step
The question
Question: find the range of f(x) = √x + 2.
f(x) = √x + 2
The range is all the answers, the y's, that can come out.
range = the y's that can come out
1 What a square root can be
A square root is never below 0.
The square root of 0 is 0.
The square root of 4 is 2.
√0 = 0, √4 = 2, √9 = 3
So √x is 0 or more.
√x ≥ 0
2 Add the 2
In f(x), + 2 comes after.
So we add 2.
We do it on both sides, so the sign stays true.
√x + 2 ≥ 0 + 2
0 plus 2 is 2.
The left side is the y.
So y ≥ 2.
The range is every y from 2 up.
y ≥ 2
3 Check
Let's check.
Put in x = 0: the inside is 0.
We get 2, the smallest y.
x = 0: y = √0 + 2 = √0 + 2 = 2
Let's look back.
First: what a square root can be.
Then: add the 2.
Last: check.
Answer
y ≥ 2