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What else can I help you with?
How are a reasonable domain and range determined for a function?
By having some knowledge about the functions involved. The natural domain is the domain for which the function is defined. For example (assuming you want to work with real numbers): The square root of x is only defined for values of x greater or equal to zero. The corresponding range can also be zero or more. The sine function is defined for all real numbers. The values the function can take (the range), however, are only values between -1 and 1. A rational function (a polynomial divided by another polynomial) is defined for all values, except those where the denominator is zero. Determining the range is a bit more complicated here.
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - a is a factor?
B
Can convergence of maclaurin series explain properties of function?
Yes, the convergence of a Maclaurin series can provide insights into the properties of a function. If the series converges to a function in a neighborhood of zero, it suggests that the function is infinitely differentiable at that point and can be approximated by polynomial terms. Additionally, the nature of convergence can reveal information about the function's behavior, such as continuity and smoothness. However, convergence does not guarantee that the series represents the function for all values, especially if the function has singularities or discontinuities elsewhere.
When the zeros of a polynomial function are 1 divided by2 and negative 1 what is the function?
Any multiple of X^2+X/2-1/2
What does it mean to solve a polynomial?
Find values of the variable for which the value of the polynomial is zero.
How do you determine the x-intercepts of the polynomial function?
set the values of the y equal to zero
How do the zeros of a polynomial function help you determine the answer?
They tell you where the graph of the polynomial crosses the x-axis.Now, taking the derivative of the polynomial and setting that answer to zero tells you where the localized maximum and minimum values occur. Two values that have vast applications in almost any profession that uses statistics.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
How do you find the y intercepts for a polynomial function?
To find the y-intercepts of a polynomial function, set the value of ( x ) to 0 and solve for ( y ). This involves substituting 0 into the polynomial equation and simplifying to find the corresponding ( y )-value. The y-intercept is the point where the graph of the function crosses the y-axis, represented as the coordinate (0, ( y )).
How do you find the factors of polynomails function of degree greater than 20?
With difficulty. Plot a graph of the polynomial and see where it crosses the x axis. If it does, then y=0 at that point, and (x-a) is a factor. Sometimes you might spot where the polynomial is zero just by trying various values.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
What is a zero of a function?
Assuming the polynomial is written in terms of "x": It means, what value must "x" have, for the polynomial to evaluate to zero? For example: f(x) = x2 - 5x + 6 has zeros for x = 2, and x = 3. That means that if you replace each "x" in the polynomial with 2, for example, the polynomial evaluates to zero.
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".
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
Example of fundamental difference between a polynomial function and an exponential function?
fundamental difference between a polynomial function and an exponential function?
