Question

For the functions below, state the amplitude, period, phase shift, and vertical translation of the graph for the sinusoid.

y=-sin(x-pi/4)+2

Answer 1

\(\Large y = \color{red}a sin[\color{blue}b(x-\color{green}c)] + \color{brown}d\)
Let's use this for example:
\(\Large\color{red}{|a|} \) is the amplitude and it indicates how far the graph is going above or below the x-axis
\(\LARGE\frac{2pi}{\color{blue}{ b}}\) is the period which determines the length where the graph repeats itself along the x-axis
\(\Large\color{green}c\) is the phase shifting, like horizontal shifting, distance from where the graph moves left or right
\(\Large\color{brown}d\) is the vertical shifting, where the distance of the graph where it moves up or down