If the area of △ AOB is 6, and Y decreases with the increase of X, try to find the following results: 1 The analytic expression of this function

If the area of △ AOB is 6, and Y decreases with the increase of X, try to find the following results: 1 The analytic expression of this function

y=kx+b
Y decreases with the increase of X
K0
Point B (0, b)
A(3,0)
S=3b/2=6
B=4
k=-4/3
y=-4x/3+4

If the area of △ AOB is 6, try to find the coordinates of point B and the analytic formula of first order function

If the coordinates of point B are (0, b), then ob = B or ob = - B, because OA = = 3, the area of △ AOB is 6,
So 3B / 2 = 6 or - 3B / 2 = 6
So B = 4 or B = - 4
B coordinate is (0,4) or (0, - 4)
The analytic formula is y = KX + B, substituting the coordinates of point a (3,0) and B into the equation system
0=3k+4,k=-4/3;
0=3k-4,k=4/3
So the analytic formula is
Y = - 4 / 3x + 4 or y = 4 / 3x-4

As shown in the figure, the image with the inverse scale function y = 2 / X and the image with the first order function y = KX + B intersect at point a (m, 2), point B (- 2, n). The intersection point of the image of the first-order function and the y-axis is C. (1) find the analytic formula of the first-order function, (2) find the coordinates of point C (3) find the area of △ AOC

(1) Replace the point a (m, 2) into the inverse proportional function y = 2 / X
2m = 2, M = 1,
Replace the point B (- 2, n) into the inverse scaling function y = 2 / X
The result is - 2n = 2 and N = - 1,
The coordinate of point a is (1,2), and that of point B is (- 2, - 1),
Substituting point a (1,2), point B (- 2, - 1) into the function of degree y = KX + B
K + B = 2, - 2K + B = - 1, k = 1, B = 1,
The analytic formula of the first order function is y = x + 1;
(2) For y = x + 1, let x = 0, then y = 1,
The coordinates of point C are (0,1),
（3）∴S△AOC=1/2×1×1=1/2；

The image of the first order function y = KX + B and the inverse scale function y = m If the image of X intersects a (- 2,1), B (1, n), then n=______ .

∵ a (- 2,1) in the inverse proportional function y = M
In the image of X,
∴1=m
- 2, M = - 2
The analytic formula of inverse proportional function is y = − 2
x，
∵ B (1, n) on the inverse proportional function h,
∴n=-2．
So the answer is: - 2

The image of the first order function y = KX + B and the image of the inverse scale function y = m / X intersect at a (- 2,1), B (1, n) (1) The analytic formula of inverse proportional function and first order function (2) When writing, the value range of X whose direct value is greater than that of inverse proportional function

(1) Therefore, the coordinate of point B is (1, - 2) first order function y = KX + B passing through a (- 2,1), B (1, - 2) two points, so the slope k = [1 - (- 2)] / (- 2-1) = - 1, so y = - (x + 2) + 1 = - X-1 inverse proportion

As shown in the figure, the image of the first order function y = KX + B and the inverse scale function y = M When the value of the first order function is greater than the value of the inverse proportional function, the value range of the independent variable x is () A. -2＜x＜1 B. 0＜x＜1 C. X ＜ - 2 and 0 ＜ x ＜ 1 D. - 2 < x < 1 and x > 1

Substitute a (- 2,1) into y = M
X: M = - 2,
That is to say, the analytic formula of inverse proportional function is y = - 2
x，
Replace B (n, - 2) with y = - 2
X is - 2 = - 2
n，
n=1，
That is, the coordinates of B are (1, - 2),
Therefore, when the value of the first-order function is greater than the value of the inverse proportional function, the value range of the independent variable x is x < 2 or 0 < x < 1,
Therefore, C

How to compare different bases of the same index in exponential function

First, if the base number is the same and the exponent is different, use the monotonicity of the exponential function; second, if the index is the same and the base is different, draw the image of two functions, such as judging 0.7 ^ (0.8) and 0.6 ^ (0.8). First draw the image of f (x) = 0.7 ^ x, G (x) = 0.6 ^ x, and observe the function when x = 0.8

How does exponential function compare to size Especially when the bottom is different Thank you very much

You can judge according to the image: when the bottom is greater than 1, the image with larger bottom is steeper. At this time, when x > 0 in the first quadrant, the function value of the bottom is large; in the third quadrant, X

How do exponential functions compare sizes For example: compare 10's 2005 times + 1 / 10 2006 times + 1 and 10 2006 times + 1 / 10 2007 times + 1 What are the other ways to do business

Haha, it's simple. The main thing you don't need to do is look at the 2005 times of 10 and the 2006 times of 10. You should know that the 2006 times of 10 are 10 times of the 2005 times of 10. In other words, the 2006 times of 10 are far larger than the 2005 times of 10. This difference is an astronomical number. However, it doesn't matter how the size of other parts is different

Exponential function comparison size Size comparison of 6 ^ 7 and 7 ^ 6 types

It's OK to calculate