Yes, a polynomial function is always continuous
True
The function is not continuous.
No it is not
A second-degree polynomial function is a function of the form: P(x) = ax2 + bx + cWhere a ≠ 0.
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.
Yes.
Yes, all polynomial functions are continuous.
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.
No. It would not be a polynomial function then.
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.
No, log n is not considered a polynomial function. It is a logarithmic function, which grows at a slower rate than polynomial functions.
A line representing any polynomial function, power function (including negative powers), trigonometric functions, most continuous probability distribution functions.
A rational function is the quotient 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".
fundamental difference between a polynomial function and an exponential function?
false
True