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
Now you Izaberite problem, ili tipkanje ili nacrtati vlastiti. Svaki korak, slika, odgovor skriven dok ne pitate.
Besplatan račun dodaje bilješke na svakoj lekciji, zapis onoga što ste završili, rješeni problemi na jednom mjestu, i tutor možete pitati o ovoj stranici. Sama matematika je otvorena za sve, potpisani ili ne.
Prijavi se PrijavaSimboli koji se koriste ovdje
Dodirnite bilo koji simbol za punu definiciju, sliku, i što znači svako slovo u njoj.
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