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Can a linear function be continuous but not have a domain and range of all real numbers?
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How do you draw a continuous linear decreasing function?
A continuous linear decreasing function is a line that goes on forever and has a negative slope (is downhill from left to right). For example, the line y = -x is a continuous linear decreasing function.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
How can you tell a linear function from an equation?
An equation is a statement that two things are equal. A function is a rule or process that gives you a value if you give it something in its domain (the set of things on which it is defined) as an argument. Functions on numbers that are defined by a rule can usually be expressed by an equation. A linear function is one that can be defined by a linear equation.
What is discrete and continuous in math?
These terms describe functions.A continuous function looks like a straight line or a curve, depending on if it is linear or quadratic.A discrete function looks like dots on a number line, only covering the integers, instead of numbers in between.
Define linear equation and function Are they the same Why or why not?
define "linear equation" and "function." * * * * * Suppose f is a mapping from one set of numbers (the "domain") to another (the "range"). The domain and range may be the same or different. If, for each and every element in the domain, f assigns one and only one elemnt in the range, then f is a function. For example, f might be "double the number and then add 23", or "square root the number and then divide by 7". In the second case, the domain cannot have any negative numbers in it (why?). A linear equation is a function of the form y or f(x) = mx + c where m and c are constants and x and y are variables. The function f maps every value of x in the domain x onto the value y according to the rule: multiply by m and add c. The equation is called linear because for any pair of values x1 and x2 and the corresponding values y1 and y2, the ratio (y2 - y1)/(x2 - x1) is the constant m.
What is the end behavior of a linear function?
Assuming the domain is unbounded, the linear function continues to be a linear function to its end.
How do you draw a continuous linear decreasing function?
A continuous linear decreasing function is a line that goes on forever and has a negative slope (is downhill from left to right). For example, the line y = -x is a continuous linear decreasing function.
What is a function that forms a line when graphed called?
It is a continuous function. If the line is a straight line, it is a linear function.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
What are the similarities between quadratic function and linear function?
Both are polynomials. They are continuous and are differentiable.
How can you tell a linear function from an equation?
An equation is a statement that two things are equal. A function is a rule or process that gives you a value if you give it something in its domain (the set of things on which it is defined) as an argument. Functions on numbers that are defined by a rule can usually be expressed by an equation. A linear function is one that can be defined by a linear equation.
What is the domain and range for the following function and its inverse f of x equals -x plus 5?
The function is a simple linear function and so its nature does not limit the domain or range in any way. So the domain and range can be the whole of the real numbers. If the domain is a proper subset of that then the range must be defined accordingly. Similarly, if the range is known then the appropriate domain needs to be defined.
What is the range of a linear function?
The range is the y, while the domain is the x.
What is discrete and continuous in math?
These terms describe functions.A continuous function looks like a straight line or a curve, depending on if it is linear or quadratic.A discrete function looks like dots on a number line, only covering the integers, instead of numbers in between.
What is a continuous group?
A group has group operations. If these operations are continuous, it is called a continuos group. Addition of the real numbers under addition with the linear topology is one example. If I apply the discrete topology to any group, I can make it continuous. Note: we need continuous function and inverse!
What is the correspondence of the domain and range of a linear function?
It is a bijection [one-to-one and onto].
What similarities and differences do you see between the function and linear equations?
Linear equations are a tiny subset of functions. Linear equations are simple, continuous functions.
