Lesson 2 You Are the Imagineer Develop Understanding

Ready

1.

The black curve in the graph shows the graph of .

a sine function graphed on a coordinate plane and two horizontal lines graphed at the minimas and maximas x–2π–2π–2π–π–π–ππππy–2–2–2222000

a.

Write the equation of the green dotted line labeled .

b.

Write the equation of the purple dotted line labeled .

c.

List everything you notice about the graphs of , , and .

2.

The black curve in the graph shows the graph of .

a sine function graphed on a coordinate plane and a horizontal line drawn through the point (0,3) x–2π–2π–2π–π–π–ππππy–2–2–2–1–1–1111222333000

a.

Write the equation of the purple line labeled .

b.

Sketch in the graph of .

a sine function graphed on a coordinate plane and a horizontal line drawn through the point (0,3) x–2π–2π–2π–π–π–ππππy–2–2–2–1–1–1111222333000

c.

What is the equation of ?

d.

Would the line also be a boundary line for your sketch? Explain.

3.

The black curve in the graph shows the graph of .

a sine function graphed on a coordinate plane and a horizontal line drawn through the point (0,-3) x–2π–2π–2π–π–π–ππππy–2–2–2222000

a.

Write the equation of the purple line labeled .

b.

Sketch in the graph of .

a sine function graphed on a coordinate plane and a horizontal line drawn through the point (0,3) x–2π–2π–2π–π–π–ππππy–2–2–2–1–1–1111222333000

c.

What is the equation of ?

d.

How is the graph of different from the graph of ?

e.

Would the line also be a boundary line for your sketch? Explain.

Set

4.

a.

Fill in the values for in the table.

b.

With a smooth curve, graph

a blank coordinate plane x–2π–2π–2π–π–π–ππππy–4–4–4–2–2–2222444000

5.

or

a.

Fill in the values for in the table.

b.

Now graph

or

.

a blank coordinate plane x–2π–2π–2π–π–π–ππππy–4–4–4–2–2–2222444000

Match each equation below with the appropriate graph. Describe the features of the graph that helped you match the equations.

A.

an irregular curved line on a coordinate plane x–10–10–10–5–5–5555101010y–5–5