Question

Please help I don't understand how to do this. The equation is
`g(x) = 5 \sin( - 2x) + 2`

Answer 1

1) Considering the parent function: f(x) = sin(x) and the function g(x)=5sin(-2x) +2

We have the following information:

g(x)=5sin(-2x) +2

Amplitude, to find that out in any function y= a.bsin(bx-c)+d the absolute value of A is the amplitude. So in this case the Amplitude is 5

Graphically

Note the midline in purple, the g(x) in green, and f(x) in blue.

• Frequency

Frequency Is the number of cycles on a certain interval. Algebraically we can find it through a formula

`f=(b)/(2\pi)\Rightarrow f=(-2)/(2\pi)=(1)/(\pi)`

• Period

A period marks the distance between a trig function starts to behave the same.

Algebraically is found by:

`P=(2\pi)/(|b|)=(2\pi)/(|-2|)=\pi`

• Phase Shift

Phase shift, by definition, is the distance a trigonometric function is shifted horizontally. Algebraically, is found by:

`\begin{gathered} Phase=(c)/(b)=(0)/(2)=0 \\ Vertical\colon\text{ d=2} \end{gathered}`

• Vertical Translation:

Since there are no Vertical asymptotes, we can state that the vertical translation doesn't exist.

• Midline

The midline of a trigonometric function marks using a horizontal line the central point where the curve oscillates. The midline is found by the vertical translation, in this case, y=2