maths.free › Precalculus › Polynomial functions
Polynomial functions
Degree, end behaviour, zeros, turning points, and what the graph must look like.
A polynomial of degree n has at most n real zeros and at most n − 1 turning points, and its ends point where the leading term sends them. Factoring finds the zeros; the derivative finds the turning points. Type a polynomial as y = … to see all of it at once.
Radni primjer · y = x^3 - 3x
Korak po korak
- x^{3} - 3 x
An expression in x. Here is what it does.
- x \left(x^{2} - 3\right)
Simplified form.
- x = 0, x = - \sqrt{3}, x = \sqrt{3}
Real zeros (where the graph crosses the axis).
- \frac{d}{dx} = 3 x^{2} - 3
Derivative (slope).
Otkrij odgovor
Sada ti Izaberite problem, ili upišite ili nacrtajte svoj, svaki korak, slika, odgovor skriven dok ga ne pitate.
Besplatni račun dodaje bilješke na svaku lekciju, zapis onoga što ste završili, vaše riješene probleme na jednom mjestu, i tutora kojeg možete pitati o ovoj stranici. Sama matematika je otvorena za svakoga, prijavljenog ili ne.
Prijavite se PrijavaSimboli korišteni ovdje
Dodirnite bilo koji simbol za potpunu definiciju, sliku i što svako slovo u njemu znači.
Kako: Polynomial functions
- An expression in x. Here is what it does.
- Simplified form.
- Real zeros (where the graph crosses the axis).
- Derivative (slope).
Pitanja koja ljudi postavljaju
What is a function, really?
A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.
Why do we need complex numbers?
Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.
Više u Precalculus
Complex numbersRational functionsSequences and seriesThe binomial theoremConic sectionsVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates