Question

State the domain and range for: y= √ x - 3+6

Answer 1

Answer:

D = {x|x∈R|x≥3}

R = {y|y∈R|y≥6}

Step-by-step explanation:

y = √(x - 3) +6

This graph type is a root graph because y = √ of something. Root graphs have a vertex point that none of the "x" and "y" values pass.

The vertex is (3, 6). Inside the root, - 3, represents the negative x value of the vertex. The x value is 3 because the inside of a root cannot equal to less than 0. If x was 3, √(x - 3) is √0. If x was 4, √(x - 3) is √(-1), an imaginary number.

The number outside of the root is the y coordinate. + 6

Since there is no negative outside the root, like -√(x - 3), the root continues to the upward, so "y" has to be greater than the y-coordinate in the vertex.

The graph continues rightward because the root is not imaginary, so x has to be greater than the x-coordinate in the vertex. An imaginary root like √-(x - 3) continues leftward.

Both "x" and "y" can also be any number, decimal or whole, so it's a real number, represented by R.

D = {x|x∈R|x≥3}

R = {y|y∈R|y≥6}