Elementary function is a difficult point in senior high school. One kind of function contains absolute value, which we generally call absolute value function, for example, f (x) = x, and its image consists of two straight lines.

There is also a slightly more complicated absolute value function, and we can still draw pictures according to the analytical formula.

F(x)= x- 1+x+2。

Let's draw an image of this function. First, turn the function into a piecewise function:

According to the different intervals of the domain, draw its image:

After painting, we can sum up that for this absolute value function, we must first find the turning point, which is actually the corresponding point coordinates when the value in the absolute value is 0. In this example, the coordinates of the turning points are (-2, 3) and (2, 3) respectively, and then the turning points are connected, and then the changing law of the function value on the left side of the left turning point and the function value on the right side of the right turning point is seen, so that the function image can be roughly judged.

This function image can be described as: positive infinity → (-2,3) → (2,3) → positive infinity.

After understanding this principle, let's look at an example.

For example, x+3+x-4 ≤9, find the range of x.

Analysis: The conventional method to solve this kind of problems is classified discussion. In three cases, it will be more troublesome to get the range of x by removing the absolute value. It is very simple to solve the problem with the absolute value function image from another angle. If you are skilled, you can actually get the answer by oral calculation.

Example video explanation process: graphic drawing method and problem-solving skills of absolute value function in high school mathematics