Cubic graphs, sketching polynomials and asymptotes
Fill in and plot a cubic table, build a polynomial graph from its roots and its y-intercept, and draw the vertical and horizontal asymptotes of a rational function as lines.
- سوريا: الصف ١١
- فلسطين: الصف ٩
- إيران: الصف ١٢
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ١٠
- روسيا: الصف ٩
- ألمانيا: الصف ١٠
- بريطانيا: السنة ١١
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
We build the graph of y = x٣ − ٣x from a table. Take care: the cube of a negative number stays negative, (−٢)³ = −٨. A cubic graph has an S shape and can cross the x-axis up to three times.
To sketch y = (x + ٢)(x − ١)(x − ٣) quickly: read the roots from the factors (x = −٢, 1, 3; the sign flips) and find the y-intercept by putting x = 0.
In y = (٢x + ١)/(x − ١) the denominator is zero at x = 1: the vertical line x = 1 is a vertical asymptote, which the curve hugs but never reaches. When x gets very large or very small the curve approaches the horizontal line y = 2 (the coefficients of x: 2 ÷ 1): a horizontal asymptote.