Properties of the primary function of the image
- The function y = kx + b (k ≠ 0), is called a linear function , also known as a linear function
- Change amount (y Function 2 - Y . 1 ) and the amount of change of the independent variable (X 2 - X . 1 ) ratio equal to a constant k
- Office take two linear P (X . 1 , Y . 1 ), Q (X 2 , Y 2 ) with Y 2 = KX . 1 + B, Y 2 = KX 2 + B, two subtraction device with Y 2 - Y . 1 = K (X 2 - X . 1 )
- Δy/Δx = (y2 - y1)/(x2 - x1)=k，或 Δy=kΔx
- When k> 0, the linear function is an increasing function; when k <0, a function is a decreasing function
- When b = 0, the proportional function becomes a linear function is an odd function; when b ≠ 0, neither odd function is an even function nor
- The intersection of the straight line y = kx + b is the x-axis (-b / k, 0), the intersection with the y-axis is (0, b)
Properties and image quadratic function
- Function AX = Y 2 + BX + C (A ≠ 0), is called the quadratic function
- If b = c = 0, then the function becomes AX = Y 2 (A ≠ 0), A> 0, the parabola opens upward; a <0, the parabola opens downward; This function is an even function, y-axis as its image Symmetry axis
- When the absolute value of x gradually decreases indefinitely, changes in the function value becomes smaller and smaller, from above the x-axis (downward) approaches the x-axis unlimited
With methods
- The image function is a parabola, the parabola vertex coordinates (h, k), the parabola axis of symmetry is a straight line x = h
- When a> 0, the parabola opens upward, the function to obtain a minimum value x = h, k = f (h); in (-∞, h] is the decreasing function, in [h, + ∞) is an increasing function on
- When a <0, the parabola opens downward, function has its maximum value at x = h, k = f (h); in (-∞,] h is an increasing function of the in [h, + ∞) is the Save function
Method of undetermined coefficients
- When a seeking function, know the general form of this function, undetermined coefficients, coefficients determined according to the determined title set conditions
