Let x=0 and get y= 1, let y=0 and get x= 1/2.

Draw a straight line when crossing (0,-1) and (-1/2,0), which is the image of y=2x- 1.

K and b determine the position of the function image.

When y=kx, y is proportional to x.

When k>0, the straight line must pass through the first and third quadrants, and y increases with the increase of x.

When k < 0, the straight line must pass through the second and fourth quadrants, and y decreases with the increase of x.

When y = kx+b.

When k>0, b>0, then the image of this function passes through the first, second and third quadrants.

When k>0, b<0, then the image of this function passes through the first, third and fourth quadrants.

When k < 0, b>0, then the image of this function passes through the first, second and fourth quadrants.

When k < 0, b<0, then the image of this function passes through the second, third and fourth quadrants.

When b>0, the straight line must pass through the first and second quadrants.

When b<0, the straight line must pass through the third and fourth quadrants.

When b=0, the straight line passes through the origin o (0,0).

At this time, when k>0, the straight line only passes through the first and third quadrants, not through the second and fourth quadrants.

When k < 0, the straight line only passes through the second and fourth quadrants and does not pass through the first and third quadrants.

Functional properties of linear functions

The change values of 1 and y are directly proportional to the corresponding change values of x, and the ratio is k.

That is: y=kx+b(k≠0)(k is not equal to 0, and k and b are constants).

2. When x=0, b is the intersection point of the function on the Y axis, and the coordinate is (0, b).

3.k is the slope of the linear function y=kx+b, and k=tanθ (the angle θ is the included angle between the linear function image and the positive direction of the X axis, θ ≠ 90).

4. When b=0 (y=kx), the image of a linear function becomes a proportional function, which is a special linear function.

5. Function image properties: When k is the same and b is not equal, the images are parallel.

When k is different and b is equal, the images intersect on the y axis.

When k is negative reciprocal, two straight lines are perpendicular.

6. When translating: add and subtract at the end, add left and subtract right in the middle.

The steps of drawing function images are: list, tracing points and connecting lines.

In mathematics, the graph (or image) of function f refers to the set composed of all ordered pairs of numbers (x, f(x)) [1]. Specifically, if x is a real number, then the function diagram is represented as a curve in the plane rectangular coordinate system.

If the function independent variable x is an ordered pair (x 1, x2) composed of two real numbers, then the graph is a set composed of all triple orders (x 1, x2, f(x 1, x2)) and presents as a curved surface (see 3D computer graphics).

Double hook function: function f(x)=ax+b/x, (a>0, b>0) is called double hook function.

The function is odd function, and the image is symmetrical about the origin. Located in the first and third quadrants.

When x>0, we can get from the basic inequality: y≥2√ab.

Take the equal sign if and only if ax=b/x, that is, x=√(b/a).

So its vertex coordinates are (√(b/a), 2√ab), and the image monotonically decreases at (0, √(b/a), and monotonically increases at (∝ (b/a),+∝).

Similarly: when x

Take the equal sign if and only if ax=b/x, that is, x=-√(b/a).

So its vertex coordinates are (-√(b/a), -2√ab),

The mirror image increases monotonically in (-∧,-√ (b/a)).

It decreases monotonically at (-√(b/a), 0).

When a<0 and b<0 can be converted into & gt0 and b>0.

Usually when drawing, x is regarded as 0. Substitute y, that is, the vertical axis coordinate (0, y)

Sometimes, the shape of y=(ax+b)/(cx+d) is regarded as an inverse proportional function through translation.

How to draw an image of a function? The function image of y=-x 1 is as follows:

When x is greater than 0, the function value y=- 1/x is less than 0, and when x tends to positive infinity, y tends to 0. When x is in the closed interval from 0 to 1, y is less than or equal to-1.

When x is less than 0, the function value y=- 1/x is greater than 0, and when x tends to negative infinity, y tends to 0. When x is in the closed interval from 0 to-1, y is greater than or equal to 1.

Extended data:

Negative x- 1 is an inverse proportional function. When drawing this kind of diagram, we should first look at the definition domain of the function. Obviously, the definition of this function is that x is not equal to 0, and then look at the value of y ... When drawing an image, try to capture as many points as possible, because it is an inverse proportional function, not a straight line, and the more points, the more accurate it is.

The inverse proportional function is a function in the form of y=k/x(k is a constant, k≠0). The range of the independent variable x is all real numbers that are not equal to 0. The image of the inverse proportional function is a hyperbola.

References:

-Functional images