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Q: A line is an for a function if the graph of the function gets closer and closer to touching the line but never reaches it?
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What is the function and the limit?

A lot of people think of a function as an "equation," but it can be more general than that. In formal definitions, a function is a "rule" that assigns every input to exactly one output. You might see a function as a graph, an equation, a table, or an obnoxious person that shouts back at you every word you say, but in pig latin. The limit of a function exists if, as the input x approaches something, the output f(x) approaches something--regardless of the output when x actually reaches the thing it approaches. The limit is the thing that f(x) approaches. For example, picture (or Google), the graph of f(x) = 1/x. As x approaches infinity (further and further to the right of the graph), the curve f(x) gets closer and closer to the x-axis--meaning it gets closer and closer to zero.


What term is used to describe a represntation of a thing or system and can be used as a way to test hypotheses?

A graph is a representation of a thing/system, and can be used to test a hypothesis. For example, if you have a graph of a trend you can find the function of that trend. Then, you can plug in values the graph defines--say, at 2 the graph reaches 5--and if the function works, you know you have modeled the phenomenon correctly. This function testing can work to test a hypothesis, especially in finding trends.


Is a circle graph a function?

No, a circle graph is never a function.


What is a line that a graph gets closer and closer to but does not touch?

Asymptote


What happens to a graph that is representative of exponential decay?

As time passes - as the graph goes more and more to the right, usually - the graph will get closer and closer to the horizontal axis.


What is the zero of a function and how does it relate to the functions graph?

A zero of a function is a point at which the value of the function is zero. If you graph the function, it is a point at which the graph touches the x-axis.


Can a line be a graph of a function?

Yes the graph of a function can be a vertical or a horizontal line


Can a line be the graph of a function?

Yes the graph of a function can be a vertical or a horizontal line


How can you tell if a graph is a sine function or a cosine function?

sine graph will be formed at origine of graph and cosine graph is find on y-axise


How is the function differentiable in graph?

If the graph of the function is a continuous line then the function is differentiable. Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point . The slope of a tangent at any point of the graph gives the derivative of the function at that point.


What is e for?

In maths, e is a representation of a number (much in the same was as the pi symbol is) of about 2.71.... It is usually raised to a power, the graph of which is a curve crossing the y axis at one; as you follow it left it gets closer and closer to y=0 but never reaches it. As you follow it right it approaches vertical, but again never reaches it. e is the inverse function of a natural logarithm so eln(x)=x and ln(ex) also equals x another important point is that the differential of ex is ex


How can you tell if a graph is a function?

A graph is a function if every input (x-value) corresponds to only one output (y-value). One way to check for this is to perform the vertical line test: if a vertical line intersects the graph at more than one point, the graph is not a function.