Question

How is the graph of y=√-2x related to its parent function, y=√x?

Answer 1

Answer:

Option D - It is horizontally compressed by a factor of 2 and reflected over the y-axis.

Step-by-step explanation:

Given : The graph of $y=\sqrt{-2x}$  related to its parent function $y=\sqrt{x}$.

To find : How is the graph translated?

Solution :

Let,

The parent function $f(x)=\sqrt{x}$

Translated function $g(x)=\sqrt{-2x}$

• In the parent function, the graph is reflected over y-axis as

The reflection of the point (x,y) across  the y-axis is the point (-x,y).

f(x,y)→f(-x,y)

$g(x)=\sqrt{-x}$

• In the parent function, the graph is horizontally compressed as

The compression horizontally the function became

y=f(x)→ y=f(bx) , b is the compression factor and b>1

$y=\sqrt{x}$ → $y=\sqrt{-2x}$ , function is compressed by 2 unit.

Therefore, Option D is correct.

It is horizontally compressed by a factor of 2 and reflected over the y-axis.

We plot the graph of both the equations in which translation is shown.

Refer the attached graph below.

Answer 2

D is correct just took