If a Graph Has a Hole Is It Continuous

The functions whose graphs are shown below are said to be continuous since these graphs have no breaks gaps or holes. A continuous function is not necessary to have vertical asymptotes.

Continuity And Ivt

Continuity can be defined conceptually in a few different ways.

. It approaches positive infinity. Which of the following is TRUE about its graph. We first start with graphs of several continuous functions.

Then the graph has hole or removable discontinuity. A function whose graph has holes is a discontinuous function. We now present examples of discontinuous functions.

The graph does not have a hole at any finite point xy. The graph of f has a vertical asymptote. It can be drawn without lifting your pen.

It has a hole or gap. BThe graph of f has a jump. A function is continuous at a particular number if three conditions are met.

Thank you this helped. The graph of f has a vertical asymptote. The graph of f has a jump.

A continuous function can be represented by a graph without holes or breaks. The example above shows a continuous piecewise function. Values of itex x itex that make the denominator zero cause the graph not to exist even if there are no common factors in the fraction.

The only difference between the slant asymptote of the rational function and the rational function itself is that the rational function isnt defined at x 2To account for this I leave a nice big open circle at the point where x 2 showing that I know that this point is not actually included on the graph because of the zero in the denominator of the rational. If f is continuous on what can you say about its graph. CThe graph of f has a vertical asymptote.

10 EXAMPLE 10 Show that there is. Select all that apply The graph of f has a hole. Select all that apply aThe graph of f has a hole.

Given that f is continuous in - A graph will have a holejumpbreak only if the function is discontinuous. Continuity can also be defined on one side of a point using a one-sided limit. Breaks gaps or points at which they are undefined.

Since itex x2 -1 itex is not a common factor the fraction cannot be reduced. A continuous function can be represented by a graph without holes or breaks. That is the graph has no holes gaps or breaks.

This problem has been solved. A function is continuous if its graph is an unbroken curve. A function whose graph has holes is a discontinuous function.

Then the graph is continuous. If a function has a hole the three conditions effectively insist that the hole be filled in with a point to be a continuous function. It is given that f is a continuous function.

If the function factors and the bottom term cancels the discontinuity at the x-value for which the denominator was. As your pre-calculus teacher will tell you functions that arent continuous at an x value either have a removable discontinuity a hole in the graph of the function or a nonremovable discontinuity such as a jump or an asymptote in the graph. A function is continuous for example if its graph can be traced with a pen without lifting the pen from the page.

A function is continuous at a particular number if three conditions are met. It represents a rational function. The graph of f has a jump.

The graph of f has a hole. 1If f is continuous on what can you say about its graph. Yes except for one hole.

A function is continuous.

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