Find the Domain and Range f(x)=(x-2)^2+2

$f (x) = {(x - 2)}^{2} + 2$

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Locate the vertex of the parabola.

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Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = 1$

$h = 2$

$k = 2$

Since the value of $a$ is positive, the parabola opens up.

Opens Up

Find the vertex $(h, k)$ .

$(2, 2)$

The range of a parabola that opens up starts at its vertex $(2, 2)$ and extends to infinity.

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${y | y \geq 2}$

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $[2, \infty), {y | y \geq 2}$

Find the Domain and Range f(x)=(x-2)^2+2

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