How to judge the parity of function quickly I don't know if it's our teacher's original creation. It's through the addition and subtraction between X coefficient and constant odd and even power. For example, y = x + 1 is a non odd and non even function, X is a subtraction of 1 at a time, constant is a = odd addition and subtraction, odd = odd principle, and odd x = odd = even principle

How to judge the parity of function quickly I don't know if it's our teacher's original creation. It's through the addition and subtraction between X coefficient and constant odd and even power. For example, y = x + 1 is a non odd and non even function, X is a subtraction of 1 at a time, constant is a = odd addition and subtraction, odd = odd principle, and odd x = odd = even principle

Odd x odd = even odd + odd = odd odd x even = odd even x even = even even even + even = even
If f (x) is an odd function, then f (- x) = - f (x), so negative is positive and multiplication is even

Write out the parity of primary function, inverse proportion function and quadratic function

The linear function is uncertain,
The inverse proportion function is odd;
A quadratic function with B = 0 is even

A function, inverse proportion function, quadratic function synthesis problem!
13. It is known that the images of the first-order function y = - x + 6 and the inverse scale function y = K / X pass through two points a and B. the abscissa of point a is x1, the abscissa of point B is X2, and 2x1-x2 = 6
(1) Find the value of K;
(2) Calculate the area of △ AOB;
(3) If a parabola with a downward opening passes through two points a and B, and the length of the line cut on the line passing through point B and parallel to OA is 2 root sign 5, try to find the analytical formula of the parabola

The images go through two points a and B
Then the equations have two solutions
y=－x+6
y=k/x
-x+6=k/x
x^2-6x+k=0
x1+x2=6
2x1－x2=6
x1=4
x2=2
y1=2
2=k/4
k=8
A(4,2) B(2,4)