Lesson 5 Don’t Break the Chain Solidify Understanding

Ready

The same sequence is shown in both a table and a graph. Indicate on the table where you see the rate of change of the sequence. Then draw on the graph where you see the rate of change.

1.

$n$	$f (n)$
$1$	$2$
$2$	$5$
$3$	$8$
$4$	$11$
$5$	$14$

2.

$n$	$f (n)$
$1$	$13$
$2$	$11$
$3$	$9$
$4$	$7$
$5$	$5$

3.

$n$	$f (n)$
$1$	$16$
$2$	$11$
$3$	$6$
$4$	$1$
$5$	$- 4$

4.

$n$	$f (n)$
$1$	$0$
$2$	$4$
$3$	$8$
$4$	$12$
$5$	$16$

Set

In the next problems, you are given various types of information. Write the recursive and explicit functions for each geometric sequence. Finally, graph each sequence, making sure you clearly label the axes.

5.

$2$ , $4$ , $8$ , $16$ , …

Recursive:

Explicit:

6.

Claire has $$ 300$ in an account. She decides she is going to take out half of what’s left in there at the end of each month.

Recursive:

Explicit:

7.

Recursive:

Explicit:

Use the middle column in each of the given tables to write the process or number patterns that relate the input to the output. Then create both a recursive and explicit function rule.

8.

a.

$n$	Process	$f (n)$
$1$		$3$
$2$		$6$
$3$		$12$
$4$		$24$

b.

Recursive:

Explicit:

9.

a.

$n$	Process	$f (n)$
$2$		$9$
$3$		$27$
$4$		$81$
$5$		$243$

b.

Recursive:

Explicit:

Go

For the following problems, two points are given. Plot and label these points on the graph. Then connect the points, draw a right triangle to represent the slope, and determine the slope.

10.

$C (- 3, 0)$ and $D (0, 5)$

Slope: $m =$

11.

$E (- 2, - 1)$ and $N (- 4, 4)$

Slope: $m =$

12.

$S (0, 3)$ and $W (1, 6)$

Slope: $m =$

Find the slope, $m$ , and the $y$ -intercept, $b$ , for each line. Then write an equation for the line.

13.

$m =$

$b =$

Equation:

14.

$m =$

$b =$

Equation:

15.

$m =$

$b =$

Equation:

16.

$m =$

$b =$

Equation: