Learning point
1
Definition of inverse proportional function
Generally speaking, it is shaped like
x
k
y
(
k
Is constant,
k
) function is called inverse proportional function, which can be obtained from the following
To understand:
⑴
x
Is an independent variable,
y
be
x
Inverse proportional function of;
(2) Independent variables
x
The value range of is
x
All real numbers, the range of function values is
y
(3) Proportional coefficient
k
It is an important part of the definition of inverse proportional function;
(4) The inverse proportional function has three expressions:
①
x
k
y
(
k
)
②
1
kx
y
(
k
)
③
k
y
x
(Fixed value)
(
k
)
5] Function
x
k
y
(
k
) and
y
k
x
(
k
) is equivalent, so when
y
be
x
inverse proportion function
When,
x
also
y
Inverse proportional function of.
(
k
Is constant,
k
) is part of the inverse proportional function, when
k=0
When,
x
k
y
, which is not an inverse ratio letter.
Count it, because the inverse proportional function
x
k
y
(
k
), there is only one undetermined coefficient, so as long as a set of corresponding values,
You can find the answer.
k
Determine the expression of the inverse proportional function.
Learning point
2
Solving inverse proportional resolution function by undetermined coefficient method
Due to the inverse proportional function
x
k
y
(
k
), there is only one undetermined coefficient, so as long as a set of corresponding values,
You can find the answer.
k
Determine the expression of the inverse proportional function.
Learning point
three
Image and drawing method of inverse proportional function
The image of inverse proportional function is a hyperbola, which has two branches, which are located in the first, third quadrant or.
The second quadrant and the fourth quadrant are symmetrical about the origin, because the independent variables act on the inverse proportional function.
x
, function
value
y
, so its image and
x
Axis,
y
There is no intersection between axes, that is, the two branches of hyperbola are infinitely close to the coordinate axis.
But never reach the coordinate axis.
The inverse proportion drawing method is divided into three steps: (1) list; (2) tracking points; (3) connection.
Pay attention to the following points when making the inverse proportional function image again:
① The values selected in the list should be selected symmetrically;
② The more values selected in the list, the more accurate the picture will be;
(3) When connecting, you must connect with smooth curves from left to right (or from right to left) according to the size of independent variables to avoid redrawing.
Folding line;
(4) When drawing an image, draw both its branches, but the image cannot intersect with the coordinate axis.
Learning point
four
Properties of inverse proportional function
☆ Regarding the properties of the inverse proportional function, we mainly study the position of the image and the increase or decrease of the function value, as shown in the following table:
proportion
function
x
k
y
(
k
)
k
about
sign
k
k
draw
nature
①
x
about
take
value
model
besiege
be
x
y
The value range of is
y
② When?
k
When,
Functional image
about
two
individual
minute
branch
minute
no
exist
sequence
The first and third quadrants, in each
In the quadrant,
y
follow
x
The increase of
Reduce.
①
x
about
take
value
model
besiege
be
x
y
The value range of is
y
②
while
k
When,
Functional image
about
two
individual
minute
branch
minute
no
exist
sequence
The second and fourth quadrants, in each
In the quadrant,
y
follow
x
The increase of
Increase.
note:
When describing the increase or decrease of the function value,
It must be pointed out that
"
exist
Within each quadrant "
Otherwise,
Generally speaking,
while
k
When,
y
follow
x
Increase or decrease ",it will be inconsistent with the facts.
The position of the inverse proportional function image and the increase and decrease of the function have inverse proportional function coefficients.
k
On the other hand,
It can also be inferred from the position of the inverse proportional function image (hyperbola) and the increase or decrease of the function.
k
A symbol of. such as
x
k
y
In the first and third quadrants, we can see that
k
inverse proportion function
x
k
y
(
k
Proportional coefficient in).
k
Absolute value of
k
The geometric meaning of.
As shown, pass through any point on the hyperbola.
P
(
x
y
) separate
x
Axis,
y
Perpendicular to the axis,
E
、
F
They are vertical feet,
rule
OEPF
S
PE
Pulse Frequency (abbreviation of pulse frequency)
y
x
Normal male karyotype
rectangle
k
☆
inverse proportion function
x
k
y
(
k
),
k
The bigger the hyperbola.
x
k
y
The farther away from the origin of coordinates;
k
The smaller it is,
hyperbola
x
k
y
The closer to the origin of coordinates.
☆
Hyperbola is a central symmetric figure, and the center of symmetry is the origin of coordinates; A hyperbola is an axisymmetric figure, and the axis of symmetry is straight.
line
y=x
And straight line
y=
-
x