How do you graph $y = \sqrt{x} - 1$ $y=sqrtx-1$ , compare it to the parent graph and what is the domain and range?

Question

How do you graph $y = \sqrt{x} - 1$ $y=sqrtx-1$ , compare it to the parent graph and what is the domain and range?

1 Answer

Impact of this question

1637 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-07T11:48:54

domain: $x \geq 0$ $x>=0$
range: $y \geq - 1$ $y>=-1$
same shape as parent function, just shifted down 1 unit.

Explanation:

Start with the parent function: $y = \sqrt{x}$ $y=sqrt(x)$ , which has domain $x \geq 0$ $x>=0$ and range $y \geq 0$ $y>=0$ .

Our new graph is of $y = \sqrt{x} - 1$ $y=sqrt(x)-1$ . The $- 1$ $-1$ represents a vertical shift of 1 unit down. It is a "rigid transformation" in that the shape of the graph remains exactly the same, you just pick up the whole thing and move it down 1 unit.

Since there is no shift left or right, the domain of $y = \sqrt{x} - 1$ $y=sqrt(x)-1$ is the same as the domain of $y = \sqrt{x}$ $y=sqrt(x)$ , so $x \geq 0$ $x>=0$ . Since everything was shifted down 1 unit, the range changes from the range of the original, $y \geq 0$ $y>=0$ , to $y \geq - 1$ $y>=-1$ , shifting it down 1 unit.

Science

Math

Humanities

... and beyond

How do you graph $y = \sqrt{x} - 1$ $y=sqrtx-1$ , compare it to the parent graph and what is the domain and range?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you graph y=√x−1y=sqrtx-1, compare it to the parent graph and what is the domain and range?

1 Answer

Explanation:

Related questions

Impact of this question

How do you graph $y = \sqrt{x} - 1$ $y=sqrtx-1$ , compare it to the parent graph and what is the domain and range?