Question

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

Answer 1

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 $F(x) = -\frac{1}{2} sin5x$----(1)

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

In the function (1)

$F(x) = -\frac{1}{2} sin5x$

Amplitude A = $\frac{1}{2}$

In the function (2)

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

So when we compare these graphs we get

$\frac{A'}{A}=\frac{4}{\frac{1}{2} }$$\frac{A'}{A}= (\frac{4}{1})(\frac{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