### Home > PC3 > Chapter 6 > Lesson 6.1.1 > Problem6-21

6-21.

Describe the transformations and sketch the graphs of the following trigonometric functions.

1.  $f(x)=-2\cos(2x)+3$

This is a cosine graph with an amplitude of $2$ and shifted up $3$ units.
Begin by sketching the midline at $y = 3$, then boundary lines $2$ units above and $2$ units below the midline.

The function is vertically reflected and has a period of $2π/2 = π$, so sketch an inverted cosine function with the correct period in between the boundary lines.

1.  $g(x)=3\sin(x-\pi)-1$

This is a sine graph with an amplitude of $3$ and shifted down $1$ unit.
Begin by sketching the midline at $y = −1$, then boundary lines $3$ units above and $2$ units below the midline.

The period of the function is unchanged from the parent function, but this curve is shifted $π$ units to the right.