Graph a vertical translation

1
EXAMPLE 1
Graph a vertical translation
Graph y 2 sin 4x 3.
SOLUTION
STEP 1
Identify the amplitude, period, horizontal shift,
and vertical shift.
STEP 2
Draw the midline of the graph, y 3.
Find the five key points.
STEP 3
2
EXAMPLE 1
Graph a vertical translation
STEP 4
Draw the graph through the key points.
3
EXAMPLE 2
Graph a horizontal translation
Graph y 5 cos 2(x 3p ).
SOLUTION
STEP 1
Identify the amplitude, period, horizontal shift,
and vertical shift.
STEP 2
Draw the midline of the graph. Because k 0, the
midline is the x-axis.
Find the five key points.
STEP 3
4
EXAMPLE 2
Graph a horizontal translation
STEP 4
Draw the graph through the key points.
5
EXAMPLE 3
Graph a model for circular motion
b. What are your maximum and minimum heights?
6
EXAMPLE 3
Graph a model for circular motion
SOLUTION
7
EXAMPLE 3
Graph a model for circular motion
8
for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION
9
for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION
10
for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION