# Lesson 3Growing, Growing DotsDevelop Understanding

Use the tables to find the indicated values.

### 1.

 $n$ $f\left(n\right)$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $-8$ $-3$ $2$ $7$ $12$ $17$ $22$ $27$ $32$ $37$

Find

Find

#### c.

Find that goes with .

#### d.

Find that goes with

### 2.

 $n$ $g\left(n\right)$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $20$ $13$ $6$ $-1$ $-8$ $-15$ $-22$ $-29$ $-36$ $-43$

Find

Find

#### c.

Find that goes with

#### d.

Find that goes with

### 3.

In the first table of values, how does differ from ? In other words, what do and mean?

### 4.

If you have a table of values like those above and you can find the value for , how would you go about finding the value of ? How do and compare to each other?

## Set

For problems 5–8, create the missing equation for the sequence based on the table, the description, or the given equation. Then decide which equation will help to find the missing term of the sequence most efficiently. Find the term and explain your choice.

### 5.

Recursive:

 term # value $1$ $2$ $3$ $4$ $10$ $13$ $16$

Explicit equation:

Find the value of the term:

Explanation:

### 6.

Explicit equation:

 term # value $1$ $2$ $\dots$ $50$ $10$ $14$ $\dots$

Recursive:

Find the value of the term:

Explanation:

### 7.

The value of the term is .

The sequence is being doubled at each step.

Explicit equation:

Recursive:

Find the value of the term:

Explanation:

### 8.

The value of the term is .

The sequence is being doubled at each step.

Recursive:

Explicit equation:

Find the value of the term:

Explanation:

Evaluate the function to determine the output.

Example:

Recall that means to replace the value of with and work the problem to find . The point would be the location on a coordinate graph where describes the location along the -axis, and is the height of the graph.

Given that and , evaluate the following functions with the indicated values.

## Go

Evaluate the following equations when . Organize your inputs and outputs into a table of values for each equation. Let be the input and be the output.

input

output

input

output

input

output

input

output

### 17.

If , what is the value of ?

### 18.

If , what is the value of ?