# Lesson 1High Noon and Sunset ShadowsDevelop Understanding

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.

#### b.

Identify the function as even, odd, or neither.

even

odd

neither

### 2.

#### a.

Sketch the inverse of the function.

#### b.

Identify the function as even, odd, or neither.

even

odd

neither

### 3.

#### a.

Sketch the inverse of the function.

#### b.

Identify the function as even, odd, or neither.

even

odd

neither

### 4.

#### a.

Sketch the inverse of the function.

#### b.

Identify the function as even, odd, or neither.

even

odd

neither

### 5.

Here are the graphs of three even functions.

#### a.

Can an even function be invertible?

## 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 .

period:

amplitude:

vertical shift:

phase shift:

equation:

### 7.

Write the equation of the graph using .

period:

amplitude:

vertical shift:

phase shift:

equation:

### 8.

Write the equation of the graph using .

period:

amplitude:

vertical shift:

phase shift:

equation:

### 9.

Write the equation of the graph using .

period:

amplitude:

vertical shift:

phase shift:

equation:

### 10.

Write the equation of the graph using .

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.

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

### 13.

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.