## Building Functions

-Explain how to find an explicit expression.

3, 6, 9, 12, 15...

Lets say that you wanted to find the explicit formula for the given sequence. Where would you start?

Since the sequence is increasing at a constant rate, we know that we can write a linear function.

First we find the slope. We do this by choosing two numbers from the sequence. We subtract the smaller number from the bigger number and divide that by subtracting their positions.

picked numbers: 3, 6

position of picked numbers: 1, 2 (respectively)

6-3 =3

2-1=1

3/1=1

Our slope is

We then find the y-intercept. To do this, we plug in known numbers to y=mx+b. We know that our slope is 3, so that will be our

3, 6, 9, 12, 15...

Lets say that you wanted to find the explicit formula for the given sequence. Where would you start?

Since the sequence is increasing at a constant rate, we know that we can write a linear function.

First we find the slope. We do this by choosing two numbers from the sequence. We subtract the smaller number from the bigger number and divide that by subtracting their positions.

picked numbers: 3, 6

position of picked numbers: 1, 2 (respectively)

6-3 =3

2-1=1

3/1=1

Our slope is

__3__.We then find the y-intercept. To do this, we plug in known numbers to y=mx+b. We know that our slope is 3, so that will be our

*m*. Then we can plug in any of the terms and their position from our sequence to*x*and*y*. You then solve for*b*, which is your y-intercept.y=mx+b

3=3(1)+b

3=3+b

0=b

3=3(1)+b

3=3+b

0=b

In this case, our intercept is at the origin. Now we put it in explicit form!

tn=3n

Unless they say use function notation, we always use subscripts for writing explicit formulas!

Unless they say use function notation, we always use subscripts for writing explicit formulas!

-Explain how to find a recursive process for the given sequence.

3, 6, 9, 12, 15...

First, you give the first number.

t1=3

Next, you see what you do to get to the next number. In this case, you are adding 3 each time. Then you write it in this fashion.

t1=3

tn=tn-1+3

3, 6, 9, 12, 15...

First, you give the first number.

t1=3

Next, you see what you do to get to the next number. In this case, you are adding 3 each time. Then you write it in this fashion.

t1=3

tn=tn-1+3

This basically says to take the nth term you are trying to find, subtract one to get the term before it, and then add 3 to that term.

## Combinations

Using the given information, solve the problems.

You are basically combining functions!

-You are given the table below:

x1 2 3 4 |
s(x)8 12 18 2 |
a(x)4 3 6 1 |

-Find p(x) where p(x)=s(x)/a(x)

x1 2 3 4 |
s(x)8 12 18 2 |
a(x)4 3 6 1 |
p(x)2 4 3 2 |

-Find g(x) where g(x)=s(x)+a(x)

x1 2 3 4 |
s(x)8 12 18 2 |
a(x)4 3 6 1 |
g(x)12 15 24 3 |

-Find z(x) where z(x)=s(x) x a(x)

x1 2 3 4 |
s(x)8 12 18 2 |
a(x)4 3 6 1 |
z(x)32 36 108 2 |

-Find c(x) where c(x)=s(x)-a(x)

x1 2 3 4 |
s(x)8 12 18 2 |
a(x)4 3 6 1 |
c(x)4 9 12 1 |

## Vertical Translations

A vertical translation is when a line is moved up or down.

We use this general formula:

f(x)=a(x-h)+k

K moves the graph vertically.

We do not worry about the other letters at this moment.

We use this general formula:

f(x)=a(x-h)+k

K moves the graph vertically.

We do not worry about the other letters at this moment.

- Lets move the line f(x)=2x vertically and find k.

1. *original line is blue*

There in NO k.

2. *Line 2 is purple*

k is now positive two because the original graphed line moved up 2 spaces.

The function would be:

f(x)=2x+2

The function would be:

f(x)=2x+2

3. *Line 3 is red*

k is now negative four because the original graphed line moved down four spaces.

The function would be:

f(x)=2x-4

The function would be:

f(x)=2x-4

4. *Line 4 is green*

k is now positive five because the original graphed line moved up five spaces.

The function would be:

f(x)=2x+5

The function would be:

f(x)=2x+5