- published: 05 Sep 2012
- views: 43003
A graph of the function cos(x) on the domain , with x-intercepts indicated in red. The function has zeroes where x is
,
,
and
.
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation
In other words, a "zero" of a function is an input value that produces an output of zero (0).
A root of a polynomial is a zero of the associated polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree and that the number of roots and the degree are equal when one considers the complex roots (or more generally the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by
has the two roots 2 and 3, since
If the function maps real numbers to real numbers, its zeroes are the x-coordinates of the points where its graph meets the x-axis. An alternative name for such a point (x,0) in this context is an x-intercept.
Use the quadratic formula to find roots of the function
Polynomial function - Finding real roots
❤︎² How to Find the Domain of Any Function (mathbff)
❖ Finding all the Zeros of a Polynomial - Example 3 ❖
Algebra 2 - Square Root Functions and Inequalities
Graphing Square Root Functions
Graphing Square Root Functions
2.2 Square Root of a Function (Pre-Caclculus 30)
Derivative of Root Function Using Definition of a Derivative
graphing cube root functions
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sullivan 9e 5-5 part 3 - example finding roots.avi
MIT grad shows a surefire way to find the domain of any function. To skip ahead: 1) For POLYNOMIAL only, skip to time 0:45. 2) For FRACTION only, skip to time 1:44. 3) For SQUARE ROOT only, skip to 5:08. 4) For SQUARE ROOT ON BOTTOM of Fraction, skip to 8:44. 5) For SQUARE ROOT ON TOP of Fraction, skip to 10:09. For Domain, you just need to watch out for Square Roots and/or Fractions! If your function is... 1) a POLYNOMIAL (no square roots or fractions), i.e. f(x) = x^2 + 3x + 1, domain is "all real numbers." 2) a FRACTION (w/ no square root), i.e. f(x) = (2x+1)/(x^2+5x+6). Set bottom "not equal" to zero. Solve for x. 3) a SQUARE ROOT (w/ no fraction), i.e. f(x) = sqrt(x+1). Set part under root "greater than or equal to zero". 4) a FRACTION w/ A SQUARE ROOT ON BOTTOM, i.e. f(x) = (x^...
Example 2: https://www.youtube.com/watch?v=Sbpo2phnKxo Finding all the Zeros of a Polynomial - Example 3. In this video, I use the rational roots test to find all possible rational roots; after finding one I use long division to factor, and then repeat! Very fun!
This video looks at graphing square root functions. It includes two examples. The graphing calculator used in the video is accessible at www.desmos.com
A lesson on graphs of square roots of functions.
Derivative of Root Functions Using Definition of a Derivative. In this video, I find the slope of a tangent line at a point for a square root function by finding the derivative using the limit definition of a derivative.
Here are some examples of how to graph cube root functions.