It is known that Y1 is equal to - x plus 3 and Y2 is equal to 3x minus 4. When x takes what value, Y1 is equal to Y2? When x goes where value, Y1 > Y2? When x takes what value, Y1

It is known that Y1 is equal to - x plus 3 and Y2 is equal to 3x minus 4. When x takes what value, Y1 is equal to Y2? When x goes where value, Y1 > Y2? When x takes what value, Y1

When Y1 and Y2 are equal, x + 3 = 3x-4 and x = 3.5
Take any number where x is less than 3.5. For convenience, take zero, then Y1 = 3, y2 = - 4, so Y1 is greater than Y2
Because it is a linear function, when x is less than 3.5, Y1 is greater than Y2. Similarly, when x is greater than 3,5, Y1 is less than Y2

Y1 = - x + 3, y2 = 3x-4, when what is the value of X, Y1 = Y2?

Because Y1 = - x + 3, y2 = 3x-4, to satisfy Y1 = Y2, we can get the formula:
-x+3=3x-4
The equation of first degree in one variable is very simple,
7＝4x
x=7/4
So when x = 7 / 4, Y1 = Y2

If Y1 = - x + 3, y2 = 3x - 4, try to determine when x takes what value, Y1 < Y2 holds?
Write down what you do and teach me not to just answer

∵y1＜y2
∴-x+3＜3x-4
∴-4x＜-7
∴x＞7/4

Given that Y1 = - 3x + 3, y2 = 3x-4, when x is any value, Y1 > Y2
Such as the title

-3x+3>3x-4
x

Parabola y = 3 (X-5) ², when x1

x1

The parabola y2 = 2px has three points a (2, Y1) B (X2, - 4) C (6, Y3), f is the focus of the parabola, and the absolute value of AF, BF, CF is the arithmetic sequence, and the values of P, X2, Y1, Y3 are obtained

The distance from any point on the parabola to the focus is equal to the distance from the point to the directrix
Guide line x = - P / 2
AF=P/2 + 2
BF=P/2 + X2
CF=P/2 + 6
The absolute value of AF BF CF is an arithmetic sequence
∴2×BF=AF+CF
∴X2=4
Substituting B (4, - 4) into Y & sup2; = 2px,
We get P = 2
Ψ Y1 = 2 × 2 under radical
Y3 = 2 × 6 under radical

Let y = ax & sup2; - ax + C have three points a (1, Y1), B (- 1, Y2), C (- 5, Y3)?

By substituting ABC three four into parabola, we get
y1=a-a+c=c
y2=a+a+c=2a+c
y3=25a+5a+c=30a+c
y2-y1=2a
y3-y2=28a
y3-y1=30a
If a is greater than 0, then y3-y1 is greater than y3-y2 is greater than y2-y1
We get that Y3 is greater than Y2 and greater than Y1
If a is less than 0, then Y3 is less than Y2 and Y1

The parabola y = ax ∧ 2-2x + 2 has three intersections with the inverse scale function y = k ∧ 2 △ X. the value range of ax ∧ 3-2x ∧ 2 + 2x-k ∧ 2 is obtained

As long as a ≠ 0, the range of ax ^ 3-2x ^ 2 + 2x-k ^ 2 is r

It is known that the image of the first-order function Y1 = ax + B intersects with the image of the inverse scale function y2 = K / X at two points a and B, and intersects with the y-axis at point P, and
The coordinates of point a are (- 4,1) and point B are (n, - 4), and O is the origin of the coordinates
(1) Analytic expressions of inverse series function and linear function
(2) When x is what value, there is y1-y2 > 0

(1) Let (- 4,1) be brought into y2 = K / X to get 1 = K / (- 4) k = - 4  y2 = - 4 / X. let (n, - 4) be brought into y2 = - 4 / X to get n = - 4 / (- 4) = 1  the coordinates of point B are (1, - 4). Let (1, - 4) (- 4,1) be brought into Y1 = ax + B to get a + B = - 4-4a + B = 1. The solution is a = - 1 b = - 3  Y1 = - x-3 (2) ∵ y1-y2 > 0 ∵ it can be seen from the image that

It is known that Y 1 = - 12x + 1, y 2 = 32x + 5. The size of Y 1 and y 2 is compared by image method

Draw the image of the function Y1 = - 12x + 1, y2 = 32x + 5, their intersection coordinates are (- 2, 2), so when x < - 2, Y1 > Y2; when x = - 2, Y1 = Y2; when X-2, Y1 < Y2