Answer:
Option 3. f(x) is g(x) stretched vertically by a factor 8 and reflected about the x axis.
Step-by-step explanation:
The given functions are [tex]F(x) = -\frac{1}{2} sin5x[/tex]----(1)
and g(x) = 4sin5x ------(2)
In the function (1)
[tex]F(x) = -\frac{1}{2} sin5x[/tex]
Amplitude A = [tex]\frac{1}{2}[/tex]
In the function (2)
g(x) = 4sin5x Amplitude A' = 4
So when we compare these graphs we get
[tex]\frac{A'}{A}=\frac{4}{\frac{1}{2} }[/tex][tex]\frac{A'}{A}= (\frac{4}{1})(\frac{2}{1})[/tex]
A' = 8A
Since the Graph number (2) is of positive sign that means Graph (1) is reflected about the x axis to get (2)
Therefore Option 3 is correct f(x) is stretched vertically by a factor of 8 and reflected by X axis
