Question

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

A) It is translated horizontally by 2 units and reflected over the x-axis.
B) It is translated horizontally by 2 units and reflected over the y-axis.
C) It is horizontally compressed by a factor of 2 and reflected over the x-axis.
D) It is horizontally compressed by a factor of 2 and reflected over the y-axis.

Answer 1

D is correct just took

Answer 2

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

Explanation:

Given : The graph of
`y=√(-2x)` related to its parent function
`y=√(x)`.

To find : How is the graph translated?

Solution :

Let,

The parent function
`f(x)=√(x)`

Translated function
`g(x)=√(-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)=√(-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=√(x)` →
`y=√(-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.