**a**linear

**inequality**on

**a**number line, use an

**open circle**for “less than” or”greater than”, and

**a closed circle**for “less than or equalto” or “greater than or equal to”. Graph the solution set of: -3< x < 4.

Keeping this in view, what does a closed dot mean in inequalities?

Here is a summary of how to graph **inequalities**:1) Draw a number line. 2) Put either an open circle or a **closeddot** above the number given. For ≤ and ≥ , use a **closeddot** to indicate the number itself is part of the solution. For< and >, use an open circle to indicate the number itself isnot part of the solution.

Similarly, what is an open circle? A closed, or shaded, **circle** is used to representthe inequalities greater than or equal to ( ) or less than or equalto ( ). The point is part of the solution. An **open circle** isused for greater than (>) or less than (<).

Secondly, what do open and closed dots on a graph mean?

A **closed** (solid) **dot means** the endpoint isincluded in the curve and an **open dot means** it isn't. It'slike the difference between “less than or equal to” and “lessthan”. In the **graph** you show, both **dots** are**open** which **means** the function doesn't have any value,so isn't defined, at x_0.

Does open circle mean parentheses?

An **open circle** shows that the number **is**not included, while a closed **circle** includes the number.When we write inequalities with interval notation,**parenthesis** and square **brackets** areused.

## Does a closed circle mean included?

**closed circles**are used to mark the end points of intervals.If the

**circle**is open, it

**means**the end point is NOT

**included**in the interval, but if the

**circle**is

**closed**, it

**means**the end point is

**included**.Consider the interval .

## How do you solve inequalities by graphing?

**There are three steps:**

- Rearrange the equation so “y” is on the left and everythingelse on the right.
- Plot the “y=” line (make it a solid line for y≤ ory≥, and a dashed line for y< or y>)
- Shade above the line for a “greater than” (y> or y≥)or below the line for a “less than” (y< or y≤).

## What are coefficients?

**coefficient**.Variables with no number have a

**coefficient**of 1. Example: xis really 1x. Sometimes a letter stands in for thenumber.

## What does an open circle mean in limits?

**open circle does mean**the function isundefined at that particular x-value. However,

**limits do**notcare what is actually going on at the value.

## What does a closed circle mean in limits?

**closed**and open

**circles**. Theopen

**circle**at a y-value

**means**that is not a value ofthe function when you plug in x. For example, f(−1)=−4since that is where the solid

**circle**is.

## Is a closed dot a bracket?

**brackets**when you want to include theendpoint, and you denote this with a

**closed**circle/

**dot**. On the other hand, if you want to exclude theendpoint, you use a parenthesis, which is shown by an opencircle.

## What is the integer?

**integer**(pronounced IN-tuh-jer) is a wholenumber (not a fractional number) that can be positive, negative, orzero. Examples of

**integers**are: -5, 1, 5, 8, 97, and 3,043.Examples of numbers that are not

**integers**are: -1.43, 1 3/4,3.14, .09, and 5,643.1.

## What are the symbols used in linear inequalities?

**inequality symbols**are <,≤, >, and ≥. To solve an

**inequality**sentence, useexactly the same procedure that you would if it were an equation,with the following exception.

## What does closed circle mean?

**circle**for “less than” or “greater than”, and a

**closed circle**for “less than or equal to” or “greater thanor equal to”.

## What are the dots on a graph called?

**graph**, also

**called**a line

**graph**, is a pictorial rendition of data in which specificvalues of a function are plotted as

**dots**on a coordinateplane. Adjacent pairs of

**dots**are connected by straightlines.

## What is a piecewise function in math?

**mathematics**, a

**piecewise**-defined

**function**(also called a

**piecewise function**or ahybrid

**function**) is a

**function**defined by multiplesub-

**functions**, each sub-

**function**applying to acertain interval of the main

**function's**domain, asub-domain.

## What does a hollow point on a graph mean?

**graph**looks like a

**hollow**circle. It represents the fact that the function approaches the

**point**, but is not actually defined on that preciseegin{align*}xend{align*} value.

## What is a spirit circle?

**Spirit Circle**is a group of people (Shamans,Healers, Mediums, Psychics and students) who are working to raisetheir vibrational levels to be able to go beyond the limitations ofthis physical world to connect with

**Spirit**such as lovedones, guides, angels, archangels or ascended masters.

## How do you graph parabolas?

**parabola**opens upward. All quadratic equations of the formy=ax2+bx+c y = a x 2 + b x + c have

**parabolic graphs**withy-intercept (0, c). However, not all

**parabolas**have xintercepts. Example 3:

**Graph**: y=2×2+4x+5 y = 2 x 2 + 4 x + 5.

## How do you find the range?

**range**of a set of data is thedifference between the highest and lowest values in the set. To

**find**the

**range**, first order the data from least togreatest. Then subtract the smallest value from the largest valuein the set.

## How do you graph a solution on a number line?

**How to Graph Inequalities**

- Find the number on the other side of the inequality sign fromthe variable (like the 4 in x > 4).
- Sketch a number line and draw an open circle around thatnumber.
- Fill in the circle if and only if the variable can also equalthat number.
- Shade all numbers the variable can be.

## How do you graph a function?

**Graphs**of

**functions**are

**graphs**ofequations that have been solved for y! The

**graph**of f(x) inthis example is the

**graph**of y = x

^{2}– 3. It iseasy to generate points on the

**graph**. Choose a value for thefirst coordinate, then evaluate f at that number to find the secondcoordinate.

## How do you find the domain?

**domain**is all realnumbers. A function with a fraction with a variable in thedenominator. To

**find**the

**domain**of this type offunction, set the bottom equal to zero and exclude the x value you

**find**when you solve the equation. A function with a variableinside a radical sign.