Question

How is the function f(x) related to the function g(x)

Answer 1

Option 3. f(x) is g(x) stretched vertically by a factor 8 and reflected about the x axis.

Explanation:

The given functions are
`F(x) = -(1)/(2) sin5x`----(1)

and g(x) = 4sin5x ------(2)

In the function (1)

`F(x) = -(1)/(2) sin5x`

Amplitude A =
`(1)/(2)`

In the function (2)

g(x) = 4sin5x Amplitude A' = 4

So when we compare these graphs we get

`(A')/(A)=(4)/((1)/(2) )`
`(A')/(A)= ((4)/(1))((2)/(1))`

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