Question

I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. The homework was a pdf so the choices can't expand, my teacher told me to just write the transformation of the given function in the format.

Answer 1

• Amplitude: 3

,

• Period: π/2

,

• Phase Shift: 1/8 (to the left)

,

• Vertical Shift: -0.5

Explanation:

Given the trigonometric function:

`y=3\sin (4x+(1)/(2))-0.5`

Comparing with the form below:

`\begin{gathered} y=A\sin (Bx-C)+D\text{ where:} \\ \text{Amplitude}=A \\ Period=(2\pi)/(B) \\ Phase\text{ Shift}=(C)/(B) \\ \text{Vertical Shift}=D \end{gathered}`

Thus, we have that:

`\begin{gathered} \text{Amplitude,}A=3 \\ Period,(2\pi)/(B)=(2\pi)/(4)=(\pi)/(2) \\ Phase\text{ Shift,}(C)/(B)=-(1)/(2)/4=-(1)/(8) \\ \text{Vertical Shift, }D=-0.5 \end{gathered}`

The phase shift, -1/8 indicates a shift to the left.