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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 graph of a polynomial function have no y-intercept?
No, the graph of a polynomial function cannot have no y-intercept. A polynomial function is defined for all real numbers, and when you evaluate it at (x = 0), you get the y-intercept, which is the value of the function at that point. Thus, every polynomial function will intersect the y-axis at least once, ensuring it has a y-intercept.
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.
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.
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.
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.
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 graph of a polynomial function have no y-intercept?
No, the graph of a polynomial function cannot have no y-intercept. A polynomial function is defined for all real numbers, and when you evaluate it at (x = 0), you get the y-intercept, which is the value of the function at that point. Thus, every polynomial function will intersect the y-axis at least once, ensuring it has a y-intercept.
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.
Is log n considered a polynomial function?
No, log n is not considered a polynomial function. It is a logarithmic function, which grows at a slower rate than 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".
