How do you find the domain and range of f(x) =sqrt(x-2)?

Mar 11, 2018

Domain $\in \left[2 , \infty\right)$

Range $\in \left[0 , \infty\right)$

Explanation:

graph{sqrt(x-2 [-10, 10, -5, 5]}

Simply draw out the function.

The standard root function is:

$y = a \cdot \sqrt{\left(x - h\right)} + k$

where $x - h \ge 0$

In a square root function, the number inside the root sign CANNOT be $< 0$

$x - 2 \ge 0$

$x \ge 2$

∴ Domain $\in \left[2 , \infty\right)$

As for range, there is no K value in the function we were given
∴ the range begins at 0 to infinity.

Range $\in \left[0 , \infty\right)$