Exponential function is a topic, even just learn~ Exponential function y = f (x), if f (- 3 / 2) = 27, find the analytic formula of the function~ Should y = a ^ x + k?

Exponential function is a topic, even just learn~ Exponential function y = f (x), if f (- 3 / 2) = 27, find the analytic formula of the function~ Should y = a ^ x + k?

Let y = a ^ X
Because f (- 3 / 2) = 27
So a ^ (- 3 / 2) = 27
a=1/9
f(x)=(1/9)^x
An exponential function is a function of the form y = a ^ X
Y = a ^ x + k is not an exponential function

Which of the following is an exponential function
(1)y=3*2^x
(2)y=(1/2)^2x
Why not the first one?

Exponential function, such as: y = a ^ x
a> 0, and a is not equal to 1
(1) It's just a variation of the exponential function. It's a composite function

The monotone increasing interval of function y = Log & nbsp; 12 (- x2 + X + 2) is______ ．

From - x2 + X + 2 > 0, we can get - 1 < x < 2, that is, the definition field of function is (- 1,2), y = Log & nbsp; 12 (- x2 + X + 2) can be seen as a composite of y = log12t and T = - x2 + X + 2, and y = log12t decreases monotonically, t = - x2 + X + 2 increases on (- 1,12) and decreases on (12,2), ∧ y = Log & nbsp; 12 (- x2 + X + 2) decreases on (- 1,12) and increases on (12,2)

Among the natural numbers larger than 2011, after being divided by 66, how many numbers have the same quotient and remainder? What is the sum of these numbers?
Some people use (31 + 32 +...) +65) * 67 = 112560, but I don't know where 67 came from

Let the quotient X and the remainder x, then 66x x = 67x > 2011, x > 30, and X is the remainder

How to transform polar parametric equations into rectangular coordinates
Seeking simplicity

How to transform polar parametric equations into rectangular coordinates
A: (1) rectangular coordinates to polar coordinates: x = ρ cos θ, y = ρ sin θ, X & # 178; + Y & # 178; = ρ & # 178;
（2） The polar coordinates are transformed into rectangular coordinates: ρ & # 178; = x & # 178; + Y & # 178;, Tan θ = Y / X;

Another line and so on, several factorization problems
A ^ + 5B ^ - 4ab-4b + 4 = 0
Two (a + b) (a + B-6) + 9 = 0
If the 48th power of 2 is divisible by two numbers between 60 and 70, then the two numbers are
If we know that a ^ + B ^ = 5, (3a-2b) ^ - (3a + 2b) ^ = - 48, then a + B ^=
It's better to have a process and do as much as you can
The first and second questions are wrong
A ^ + 5B ^ - 4ab-4b + 4 = 0, find a + B
If two (a + b) (a + B-6) + 9 = 0 and a ^ B ^ - 4AB + 4 = 0, then a ^ + B^=
Note "＾ is the square sign

1、a^2＋5b^2－4ab－4b＋4＝(a^2－4ab＋4b^2)＋(b^2－4b＋4)＝(a－2b)^2＋(b－2)^2＝0
So, a-2b = 0, B-2 = 0, so a = 4, B = 2
So, a + B = 6
2. (a + b) (a + B-6) + 9 = (a + b) ^ 2-6 (a + b) + 9 = (a + B-3) ^ 2 = 0, so a + B = 3
A ^ 2 × B ^ 2-4ab + 4 = (ab-2) ^ 2 = 0, so AB = 2
From a + B = 3, ab = 2, a = 1, B = 2, or a = 2, B = 1
So, a ^ 2 + B ^ 2 = 5
3. Because x ^ 8-1 = (x ^ 4 + 1) (x ^ 4-1) = (x ^ 4 + 1) (x ^ 2 + 1) (x ^ 2-1) = (x ^ 4 + 1) (x ^ 2 + 1) (x-1)
Therefore, 2 ^ 48-1 = (2 ^ 6) ^ 8-1 = 64 ^ 8-1 = (64 ^ 4 + 1) (64 ^ 2 + 1) × (64 + 1) × (64-1) = (64 ^ 4 + 1) (64 ^ 2 + 1) × 65 × 63
So the two numbers between 60 and 70 are 65 and 63
4. (3a-2b) ^ 2 - (3a + 2b) ^ 2 = - 24ab = - 48, so AB = 2
A ^ 2 + B ^ 2 = (a + b) ^ 2-2ab = (a + b) ^ 2-4 = 5, so a + B = ± 3
From a + B = 3, ab = 2, a = 1, B = 2 or a = 2, B = 1, so a + B = 3
From a + B = - 3, ab = 2, a = - 1, B = - 2 or a = - 2, B = - 1, so a + B = - 3
Therefore, a + B = ± 3

If the right angle vertex o of the isosceles right triangle AOB with the right angle side length of 2 is at the origin of the right angle coordinate system and the edge OA is on the coordinate axis, then the coordinates of point B may be -?

(0,2)(0,-2)(2,0)(-2,0)

X ^ 2-1 / x ^ 2 + 4x + 4 ÷ (x + 1) × x ^ 2 + 3x + 2 / X-1 calculation

=(x+1)(x-1)/(x+2)²×1/(x+1)×(x+2)(x+1)/(x-1)
=(x+1/(x+2)

The image of y = KX + B passes through the intersection of y = x ^ - 2x - 2 and Y axis and the vertex of the parabola. The analytic expression of this function is obtained

Y = x-2x-2
The focus on the y-axis is (0, c) = (0, - 2)
Vertex formula y = (x-1) M3-3
So vertex (1, - 3)
Y = KX + B substitute the two points above
K = - 1
B=-2
So y = - X-2

Is there a formula for chasing and meeting problems?

5、 Travel problems
1. Encounter problem
Distance sum = speed sum × encounter time
2. Problems
Distance difference = speed difference × tracking time
3. Running water
Downstream speed = ship speed + water speed
Speed against water = ship speed water speed
Ship speed = (downstream speed + upstream speed) △ 2
Water velocity = (downstream velocity upstream velocity) △ 2
4. Meet many times
Linear distance: the total number of a and B = Times of meeting × 2-1
Circular route: the total number of trips of Party A and Party B = the number of encounters
Among them, a's total distance = the distance traveled in a single journey × the total number of trips
5. Circular runway
6. Application of positive and negative proportional relation in the travel problem
A certain distance, speed and time are inversely proportional
Speed is constant, distance is proportional to time
Time is fixed, distance is proportional to speed
7. Catch up problems on the clock face
① The hour hand is in line with the minute hand;
② The hour hand is at right angles to the minute hand
8. Combine some types of score, engineering, and sum difference problems
9. The thinking methods of "back of time" and "assumed view" are often used in the itinerary problem