Question

how to determine range of a function?
example (x-2)^2 + 2

Answer 1

What is the smallest value of (x-2)^2 ?

Answer 2

When something is squared, it is always \(\ge 0\).
So \((x-2)^2 \ge 0\). Its lowest value is 0 and it occurs when x = 2.

Answer 3

how about the domain of the same function

Answer 4

So the smallest value of \((x-2)^2 + 2\) is 2.

Answer 5

Range is [2, infinity)

Answer 6

actually something with a square root would help me better with the domain

Answer 7

Is there any restriction that we should place on x?
Is there ny value of x for which \((x-2)^2 + 2\) cannot be calculated?

Answer 8

so lets say instead of (x-2)^2 it's \[\sqrt{x-2}\]

Answer 9

Since for real values, we cannot take the square root of a number < 0, we must say \(x-2 \ge 0\) or \(x \ge 2\) is the domain.

Answer 10

alright that makes sense

Answer 11

In interval notation we would write the domain as: [2, infinity)