Respuesta :
Answer: C) -1/2 f(x)
Step-by-step explanation:
vertical stretch by a factor of 2 means that the stretch occured at Y - axis.
Then h(x) will transform to 2h(x)
It followed by a reflection in the X-axis of the function F(x)
Then 2h(x) will transform to - 2h(x)
Where F(x) = - 2h(x)
Make h(x) the subject of the formula
h(x) = - 1/2f(x)
C is the correct answer
The function [tex]h[/tex]([tex]x[/tex]) after the vertical stretched by a factor of two and followed by a reflection in the X- axis will be,
[tex]h(x)=-\dfrac{1}{2}f(x)[/tex]
- Vertical stretch-When a function is multiplied by a number it stretch or shrink vertical or horizontal. If such function when multiplied by a number and stretch vertical then it is called as vertical stretch .
- In the problem the function [tex]h(x)[/tex] is stretch by a factor of 2. It is followed by a reflection in the X-axis of the function [tex]F[/tex] ([tex]x[/tex]). Vertical stretch by a factor of 2 refer that the stretch arise along the Y-axis. Thus this function will transform with twice factor. The value of function [tex]h(x)[/tex] will become,
[tex]f(x)=2h(x)[/tex]
Now the reflection arise along the X- axis. Thus the above function will reflect and the value of it will become,
[tex]f(x)=-2h(x)[/tex]
Rewrite the equation,
[tex]h(x)=\dfrac{-f(x)}{2}[/tex]
[tex]h(x)=-\dfrac{1}{2}f(x)[/tex]
Hence the function [tex]h[/tex]([tex]x[/tex]) after the vertical stretched by a factor of two and followed by a reflection in the X- axis will be,
[tex]h(x)=-\dfrac{1}{2}f(x)[/tex]
For more about the stretch factor follow the link below-
https://brainly.com/question/10488556
