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Are all polynomial funcions continuous?
Yes, all polynomial functions are continuous.
What value of a polynomial is a value for which the polynomial is smaller than any other nearby values?
A local minimum.
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 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.
How do you find the y interecepts for polynomial functions?
You set x = 0 and evaluate the polynomial. Note that this should be "y-intercept" in the singular, not in the plural.
What is zeros of the polynomial?
The zeros of a polynomial are the values of the variable for which the polynomial evaluates to zero. These values are also known as the roots or solutions of the polynomial equation. Finding the zeros is essential for understanding the behavior of the polynomial graph, including its intercepts with the x-axis. The zeros can be determined using various methods, such as factoring, the quadratic formula, or numerical techniques.
What is the difference in evaluating a polynomial and solving a polynomial?
Evaluating a polynomial is finding the value of the polynomial for a given value of the variable, usually denoted by x. Solving a polynomial equation is finding the value of the variable, x, for which the polynomial equation is true.
What are some similarities between rational functions and polynomial function?
Rational functions and polynomial functions both involve expressions made up of variables raised to non-negative integer powers. They can have similar shapes and behaviors, particularly in their graphs, where they may exhibit similar end behavior as the degree of the polynomial increases. Additionally, both types of functions can be manipulated algebraically using addition, subtraction, multiplication, and division, although rational functions can include asymptotes due to division by zero, which polynomial functions do not have. Both functions can also be analyzed using techniques such as factoring and finding roots.
What is the relationship between zeros and factors?
Zeros and factors are closely related in polynomial functions. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero, while a factor is a polynomial that divides another polynomial without leaving a remainder. If ( x = r ) is a zero of a polynomial ( P(x) ), then ( (x - r) ) is a factor of ( P(x) ). Thus, finding the zeros of a polynomial is equivalent to identifying its factors.
What is the end behavior?
End behavior refers to the behavior of a function as the input values approach positive or negative infinity. It describes how the output values (y-values) behave in these limits, often determined by the leading term of a polynomial or the dominant term in other functions. For example, in a polynomial function, if the leading coefficient is positive, the function will rise to infinity as x approaches positive infinity, and the end behavior can vary based on the degree of the polynomial. Understanding end behavior is crucial for sketching graphs and analyzing functions.
Are all polynomial funcions continuous?
Yes, all polynomial functions are continuous.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
What does it mean to solve a polynomial?
Find values of the variable for which the value of the polynomial is zero.
Who discovered polynomial?
In the 1880s, Poincaré created functions which give the solution to the order polynomial equation to the order of the polynomial equation
How do you do a polynomial?
Basically the same way you graph most functions. You can calculate pairs of value - you express the polynomial as y = p(x), that is, the y-values are calculated on the basis of the x-values, you assign different values for "x", and calculate the corresponding values for "y". Then graph them. You can get more information about a polynomial if you know calculus. Calculus books sometimes have a chapter on graphing equations. For example: if you calculate the derivative of a polynomial and then calculate when this derivate is equal to zero, you will find the points at which the polynomial may have maximum or minimum values, and if you calculate the derivative at any point, you'll see whether the polynomial increases or decreases at that point (from left to right), depending on whether the derivative is positive or negative. Also, if you calculate when the second derivative is equal to zero, you'll find points at which the polynomial may change from convex to concave or vice-versa.
How do you graph a polynomial?
Basically the same way you graph most functions. You can calculate pairs of value - you express the polynomial as y = p(x), that is, the y-values are calculated on the basis of the x-values, you assign different values for "x", and calculate the corresponding values for "y". Then graph them. You can get more information about a polynomial if you know calculus. Calculus books sometimes have a chapter on graphing equations. For example: if you calculate the derivative of a polynomial and then calculate when this derivate is equal to zero, you will find the points at which the polynomial may have maximum or minimum values, and if you calculate the derivative at any point, you'll see whether the polynomial increases or decreases at that point (from left to right), depending on whether the derivative is positive or negative. Also, if you calculate when the second derivative is equal to zero, you'll find points at which the polynomial may change from convex to concave or vice-versa.
What are Similarities of polynomial and non polynomial?
None, except that they are functions of one or more variables.
