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Lesson 1 High Noon and Sunset Shadows Develop Understanding

Ready

Sketch the inverse of the function on the same set of axes. Finally, identify each function as even, odd, or neither.

1.

a.

Sketch the inverse of the function.

a curved line with ends pointing in opposite direction is graphed on a coordinate plane x–2–2–2–1–1–1111222y–2–2–2–1–1–1111222000

b.

Identify the function as even, odd, or neither.

A.

even

B.

odd

C.

neither

2.

a.

Sketch the inverse of the function.

a straight line with a negative slope going through the points (0,0) and (0.2,-1.2) is graphed on a coordinate plane x–2–2–2–1–1–1111222y000

b.

Identify the function as even, odd, or neither.

A.

even

B.

odd

C.

neither

3.

a.

Sketch the inverse of the function.

a curved line with ends pointing in opposite direction is graphed on a coordinate plane x–2–2–2–1–1–1111222y–1–1–1111000

b.

Identify the function as even, odd, or neither.

A.

even

B.

odd

C.

neither

4.

a.

Sketch the inverse of the function.

a curved line with ends pointing in opposite direction is graphed on a coordinate plane x–2–2–2–1–1–1111222y–2–2–2–1–1–1111000

b.

Identify the function as even, odd, or neither.

A.

even

B.

odd

C.

neither

5.

Here are the graphs of three even functions.

a curved line representing a quartic function with ends pointing in the same direction is graphed on a coordinate plane x–2–2–2–1–1–1111222y–1–1–1111000
a parabola with a vertex at (0,0) opening in an upward direction on a coordinate plane x–1–1–1111y111000
an absolute value function opening up is graphed on a coordinate plane x–2–2–2–1–1–1111222y–1–1–1111000

a.

Can an even function be invertible?

b.

Justify your answer.

Set

State the period, amplitude, vertical shift, and phase shift of the function shown in the graph. Then, write the equation.

6.

Write the equation of the graph using .

a curved line representing a sine function is graphed on a coordinate plane x–2π–2π–2π–π–π–ππππ2π2π2πy–5–5–5555000

period:

amplitude:

vertical shift:

phase shift:

equation:

7.

Write the equation of the graph using .

a curved line representing a sine function is graphed on a coordinate plane with a point at (0,-3)x–2π–2π–2π–π–π–ππππ2π2π2πy–5–5–5000

period:

amplitude:

vertical shift:

phase shift:

equation:

8.

Write the equation of the graph using .

a curved line representing a cosine function is graphed on a coordinate plane x–2π–2π–2π–π–π–ππππ2π2π2πy–2–2–2222444000

period:

amplitude:

vertical shift:

phase shift:

equation:

9.

Write the equation of the graph using .

a curved line representing a wide cosine function is graphed on a coordinate plane x–2π–2π–2π–π–π–ππππ2π2π2πy–2–2–2222000

period:

amplitude:

vertical shift:

phase shift:

equation:

10.

Write the equation of the graph using .

a curved line representing a sine function is graphed on a coordinate plane with a point at (0,4)x–2π–2π–2π–π–π–ππππ2π2π2πy–4–4–4–2–2–2222444000

period:

amplitude:

vertical shift:

phase shift:

equation:

11.

The cofunction identity states that . How does this identity relate to the graph in problem #10?

Explain where you would see this identity in a right triangle.

Describe the relationships between the graphs of — solid and — dotted. Then, write their equations.

12.

a curved line representing a sine function is graphed on a coordinate plane. the same function is drawn one unit to the rightx–2π–2π–2π–π–π–ππππ2π2π2πy–2–2–2222000

Describe the relationship between the graphs of (solid) and (dotted).

13.

a curved line representing a wide sine function is graphed on a coordinate plane. another sine function is graphed but it wider.x–2π–2π–2π–π–π–ππππ2π2π2πy–2–2–2222000

Describe the relationships between the graphs of (solid) and (dotted).

14.

This graph could be interpreted as a shift or a reflection. Write the equations both ways.

a curved line representing a sine function is graphed on a coordinate plane. The same function is reflected over the x axis with an amplitude that is 1 unit more. x–2π–2π–2π–π–π–ππππ2π2π2πy–2–2–2222000

Describe the relationships between the graphs of (solid) and (dotted).

15.

a curved line representing a sine function is graphed on a coordinate plane. the same function is drawn a quarter pi to the leftx–2π–2π–2π–π–π–ππππ2π2π2πy222000

Describe the relationships between the graphs of (solid) and (dotted).

Sketch the graph of the function.

(Include two full periods. Label the scale of your horizontal axis.)

16.

a blank 17 by 17 grid

17.

a blank 17 by 17 grid

Go

Name two angles of rotation for that have the given trig ratio. .

18.

19.

20.

21.

22.

23.

24.

For which angles of rotation does ?