# graph open circle closed circle

## open circle and closed circle on graph

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## What is the difference between an open circle and a closed circle when graphing inequalities?

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( ) or less than or equal to ( ). The point is part of the solution. An open circle is used for greater than (>) or less than (<).

## What does a solid circle mean on a number line?

Inequalities on a number line Note: the open circle above a number means it is not included as part of the solution to the inequality while the solid circle means that it is. The examples below how inequalities can represent a range of solutions with an upper and lower limit.

## What does or and and mean in inequalities?

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. “Or” indicates that, as long as either statement is true, the entire compound sentence is true.

## What do open and closed circles mean in inequalities?

A closed circle indicates “greater than or equal to” or “less than or equal to,” while and open circle indicates “greater than” or “less than”.

## Is the circle open or closed for inequalities?

When graphing 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 equal to” or “greater than or equal to”.

## How do you know if the dot is open or closed?

Put either an open circle or a closed dot above the number given. For ≤ and ≥ , use a closed dot to indicate the number itself is part of the solution. For < and >, use an open circle to indicate the number itself is not part of the solution.

## Does an open dot mean equal to?

A solid dot on a number line graph indicates that the given number should be included as a possible solution, whereas an open dot indicates that the given number cannot be a solution. For example, if you graph x > 7, you place an open dot at 7 because it’s not a valid answer (7 is not greater than itself).

## Does a closed circle mean included?

When we graph inequalities on a number line, circles are used to show if a number is included or not. 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 are used.

## When graphing an inequality What does a closed circle mean?

Graph An Inequality With A Number Line : Example Question #1 Explanation: A closed circle indicates “greater than or equal to” or “less than or equal to,” while and open circle indicates “greater than” or “less than”.

## What does a closed and open circle mean on a number line?

Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).

## What does closed circle mean in limits?

The limit exists because the same y-value is approached from both sides. It does not have two locations because the open circle is a just gap in the graph. The closed circle is the actual y-value for when x=7.

## Can a limit exist when there is an open circle?

Nope. The open circle does mean the function is undefined at that particular x-value. However, limits do not care what is actually going on at the value.

## Can a limit exist at an open circle?

An open circle (also called a removable discontinuity) represents a hole in a function, which is one specific value of x that does not have a value of f(x). So, if a function approaches the same value from both the positive and the negative side and there is a hole in the function at that value, the limit still exists.

## Is there a limit if there is a hole?

If there is a hole in the graph at the value that x is approaching, with no other point for a different value of the function, then the limit does still exist.

## How do you tell if a limit does not exist?

Limits & Graphs

1. If the graph has a gap at the x value c, then the two-sided limit at that point will not exist.
2. If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.

## What happens if a limit equals 0?

So the limit is zero. Here the denominator increases more rapidly than the numerator, so the fraction gets smaller and smaller tending to zero. This happens if, for example, the power of the denominator, g(x), is greater than the power of the numerator, f(x).

## What happens if the numerator is 0?

A numerator is allowed to take on the value of zero in a fraction. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero. all have a fraction value of zero because the numerators are equal to zero. Answer.

## Can a numerator be negative?

Usually, the negative sign is placed in front of the fraction, but you will sometimes see a fraction with a negative numerator or denominator. If both the numerator and denominator are negative, then the fraction itself is positive because we are dividing a negative by a negative.

## Can fractions be zero?

Fractional Notation for Zero has no shaded parts and may be written in fraction form as . If we divide an object into n parts and take none of them, we get 0.

## What is the slope of the denominator is 0?

If the denominator of the fraction is 0, the slope is undefined. This occurs if the x value is the same for both points. The graph would be a vertical line and would indicate that the x value stays constant for every value of y.

## What is not a type of slope?

An undefined slope or infinite slope, means the line is neither moving to the left nor to the right such as the case of a vertical line.