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What are the characteristics of a polynomial function?
Some of the characteristics of such a function are:The function is continuous (it doesn't make sudden jumps)The derivative is continuous (the function doesn't suddenly change its direction)The function is unbounded - as "x" grows larger and larger, f(x) approaches either plus or minus infinity (i.e., it grows without bounds).In the complex numbers, any polynomial has at least one zero.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
Which line has no endpoint and goes on forever?
A line representing any polynomial function, power function (including negative powers), trigonometric functions, most continuous probability distribution functions.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
Are all polynomial funcions continuous?
Yes, all polynomial functions are continuous.
How different polynomial and non polynomial?
Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x". * The polynomial makes is continuous; i.e., it doesn't make sudden "jumps". * Similarly, the first derivative, the second derivative, etc., are continuous. A non-polynomial function may not have all of these properties; for example: * A rational function is not defined at any point where the denominator is zero. * The square root function is not defined for negative values. * The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0. * The function that takes the integer part of any real number makes sudden jumps at all integers.
What are the characteristics of a polynomial function?
Some of the characteristics of such a function are:The function is continuous (it doesn't make sudden jumps)The derivative is continuous (the function doesn't suddenly change its direction)The function is unbounded - as "x" grows larger and larger, f(x) approaches either plus or minus infinity (i.e., it grows without bounds).In the complex numbers, any polynomial has at least one zero.
Polynomials and non polynomials how different?
Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x". * The polynomial makes is continuous; i.e., it doesn't make sudden "jumps". * Similarly, the first derivative, the second derivative, etc., are continuous. A non-polynomial function may not have all of these properties; for example: * A rational function is not defined at any point where the denominator is zero. * The square root function is not defined for negative values. * The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0. * The function that takes the integer part of any real number makes sudden jumps at all integers.
How different polynomials and non polynomials?
Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x". * The polynomial makes is continuous; i.e., it doesn't make sudden "jumps". * Similarly, the first derivative, the second derivative, etc., are continuous. A non-polynomial function may not have all of these properties; for example: * A rational function is not defined at any point where the denominator is zero. * The square root function is not defined for negative values. * The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0. * The function that takes the integer part of any real number makes sudden jumps at all integers.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
How different the polynomials and non polynomials?
Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x". * The polynomial makes is continuous; i.e., it doesn't make sudden "jumps". * Similarly, the first derivative, the second derivative, etc., are continuous. A non-polynomial function may not have all of these properties; for example: * A rational function is not defined at any point where the denominator is zero. * The square root function is not defined for negative values. * The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0. * The function that takes the integer part of any real number makes sudden jumps at all integers.
Which line has no endpoint and goes on forever?
A line representing any polynomial function, power function (including negative powers), trigonometric functions, most continuous probability distribution functions.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
How is a rational function the ratio of two polynomial functions?
That's the definition of a "rational function". You simply divide a polynomial by another polynomial. The result is called a "rational function".
