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Exponents

Exponent Lesson
Today, you will be able to Evaluate Exponential Expressions


Write the following definitions in your math journal.

Exponent

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The exponent of a number shows you how many times the number is to be used in a multiplication.

It is written as a small number to the right and above the base number.

In this example: 82 = 8 × 8 = 64

(Another name for exponent is index or power)

Function

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A function is a special relationship between values: Each of its input values gives back exactly one output value.

It is often written as "f(x)" where x is the value you give it.

Example: 

f(x) = x/2 ("f of x is x divided by 2") is a function, because for every value of "x" you get another value "x/2", so:

* f(2) = 1
* f(16) = 8
* f(-10) = -5

Evaluate

To calculate the value of.

Example: Evaluate the cost of each pie if 3 pies cost $6. Answer: $2 each.

Expression

Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

Example 2×3 is an expression

Substitution

In Algebra "Substitution" means putting numbers where the letters are:

Example: If x=5, then what is x + 10/x ?

Put "5" where "x" is: 5 + 10/5 = 7

Set

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A collection of "things" (objects or numbers, etc).

Each member is called an element of the set.

There should be only one of each member (all members are unique).

Here is a set of clothing items.

Another Example: {1,2,3,4} is the set of counting numbers less than 5

Domain of a function

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All the values that go into a function

The output values are called the range.

Domain -> function -> Range

Example: if the function f(x) = x2 is given the values x = {1,2,3,...} then {1,2,3,...} is the domain.

Graph

Picture
A diagram of values, usually shown as lines or bars.

Order of Operations

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The rules of which calculation comes first in an expression

They are:
. do everything inside parentheses first: ()
. then do exponents, like x2
. then do multiplies and divides from left to right
. lastly do the adds and subtracts from left to right

Example: 5 × (3 + 4) - 2 × 8 = 5 × 7 - 2 × 8 = 35 - 16 = 19

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