Lesson 3 Growing, Growing Dots Develop Understanding

Ready

Use the tables to find the indicated values.

1.

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

a.

Find $f (5)$

b.

Find $f (9)$

c.

Find $n$ that goes with $f (n) = 22$ .

d.

Find $n$ that goes with $f (n) = - 3$

2.

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

a.

Find $g (3)$

b.

Find $g (8)$

c.

Find $n$ that goes with $g (n) = - 1$

d.

Find $n$ that goes with $g (n) = - 43$

3.

In the first table of values, how does $n$ differ from $f (n)$ ? In other words, what do $n$ and $f (n)$ mean?

4.

If you have a table of values like those above and you can find the value for $f (n)$ , how would you go about finding the value of $f (n - 1)$ ? How do $f (n)$ and $f (n - 1)$ 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: $now = previous term + 3$

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

Explicit equation:

Find the value of the $4 th$ term:

Explanation:

6.

Explicit equation: $f (n) = 4 n + 6$

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

Recursive:

Find the value of the $50 th$ term:

Explanation:

7.

The value of the $2 nd$ term is $24$ .

The sequence is being doubled at each step.

Explicit equation: $f (n) = 6 (2^{n})$

Recursive:

Find the value of the $3 rd$ term:

Explanation:

8.

The value of the $3 rd$ term is $12$ .

The sequence is being doubled at each step.

Recursive: $now = previous term \times 2$

Explicit equation:

Find the value of the $10 th$ term:

Explanation:

Evaluate the function to determine the output.

Example:

Recall that $f (2)$ means to replace the value of $n$ with $2$ and work the problem to find $f (n)$ . The point $(n, f (n))$ would be the location on a coordinate plane where $n$ describes the location along the $x$ -axis, and $f (n)$ is the height of the graph.

Given that $f (n) = 3 {(2)}^{n}$ and $g (n) = 8 {(5)}^{n}$ , evaluate the following functions with the indicated values.

9.

$f (5) =$

10.

$g (0) =$

11.

$f (2) =$

12.

$g (3) =$

Go

Evaluate the following equations when $x = {1, 2, 3, 4, 5}$ . Organize your inputs and outputs into a table of values for each equation. Let $x$ be the input and $y$ be the output.

13.

$y = 3 x + 5$

$x$ input	$y$ output
$1$
$2$
$3$
$4$
$5$

14.

$y = 3 {(4)}^{x}$

$x$ input	$y$ output
$1$
$2$
$3$
$4$
$5$

15.

$y = - 3^{x}$

$x$ input	$y$ output
$1$
$2$
$3$
$4$
$5$

16.

$y = {(- 3)}^{x}$

$x$ input	$y$ output
$1$
$2$
$3$
$4$
$5$

17.

If $f (n) = 5^{n}$ , what is the value of $f (4)$ ?

18.

If $g (n) = 7^{n}$ , what is the value of $g (2)$ ?