matlab plotting binary primary function image_[8th grade math] Required Knowledge Points of Primary Functions (Lower)

Example 1:

Knowing that the intersection of the image of the primary function y = 3x + m and the image of the primary function y = 4 - 2x is on the x-axis, find the value of m.

Analysis:

In this question, the functional expression of y = 4-2x is determined, then the coordinates of its intersection with the x-axis are determined, therefore, only the coordinates of the point need to be found, and substituting into y = 3x + m, the value of m can be found.

Answer:

∵ Let y = 4 - 2x = 0, x = 2.

∴ intersection (2, 0).

Substituting (2, 0) into y = 3x + m gives that

3×2＋m＝0，m＝－6．

Example 2:

Analysis:

Obviously, the intersection of the two lines and the y-axis are (0, -3), (0, 2), so only possible to intersect in the x-axis, respectively, calculate the coordinates of the intersection of the two lines and the x-axis, to get the ratio of a and b.

Answer:

Example 3:

If the points (x, y) having the solution of the quadratic equation 2x - y + b = 0 as their coordinates are all on the image of the function y = 2x - b + 1, then the constant b = _______.

Analysis:

From the question, the binary equation 2x - y + b = 0 is deformed and written in the form of a primary function, which must be consistent with the function y = 2x - b + 1, so that b can be found.

Answer:

2x－y＋b＝0，y＝2x＋b，

∴2x＋b＝2x－b＋1

-b + 1 = b, solving for b = 0.5.

Example 4:

Knowing that the intersection of the image of the primary function y = 2x + 1 and the image of the primary function y = 3x + b is in the third quadrant, find the range of b.

Analysis:

In this question, you need to combine the two primary functions into a system of equations, express the coordinates of the intersection point in an algebraic equation containing b, and then determine the range of b by obtaining a set of inequalities about b based on the coordinate identities of the points in the third quadrant.

Answer:

Example 5:

Regardless of the value of m, the intersection of the image of the primary function y = x + 2m with the image of y = -x + 4 cannot be in which quadrant?

Analysis:

If this problem is the same as in Example 4, the first two primary functions system of equations, with m containing the algebraic expression of the coordinates of the point of intersection, to discuss the range of m in each case, it is very cumbersome. Careful observation, it can be seen that the image of the line y = -x + 4 is determined, does not pass through the third quadrant, so no matter what value of m, the intersection of the two function images will not pass through the third quadrant.

Answer:

Third quadrant.

Example 6:

Analysis:

In this problem, the equation had to be solved first to express the values of x and y in terms of algebraic expressions containing a. Then x and y were analyzed for positivity and negativity to determine the quadrant through which they do not pass.

Answer:

Example 1:

As shown in the figure, if the image of the primary function y = -2x + b intersects the y-axis at the point A(0, 3), then the solution set of the inequality -2x + b > 0 is ________.

Analysis:

First, according to the coordinates of the point A, determine the linear analytic formula, the inequality -2x + b > 0, indicating that the value of y is positive, then the corresponding function image is a straight line falls above the x-axis of the portion, and the requirements of the range of values of the corresponding x, then the demand for the function image and the x-axis intersection of the transverse coordinates of the intersection of the point to derive the critical point of the left side or the right side of the critical point.

Answer:

Example 2:

The image of the function y = ax + b passes through the first, second and third quadrants and intersects the x-axis at the point (-2, 0), find the solution set of ax > b. ______.

Analysis:

We can start by roughly drawing the image of y = ax + b. Asking for the solution set of ax > b, that is, asking for the solution set of ax - b > 0, translates into asking for the range of x in the portion of the corresponding image of the function y = ax - b where the line falls above the x-axis, and drawing the image of y = ax - b, which is parallel to y = ax + b parallel to the intersection with the y-axis (0, -b), which leads to the intersection with the x-axis (2, 0).

Answer:

Example 3:

Analysis:

First use the method of constant coefficients to find the coordinates of point A, -2x > ax + 3.

Denote y1 > y2, i.e., the image of the function y1 has to be above the image of the function y2 to determine the solution set of x.

Answer:

Example 4:

Analysis:

Requiring a solution to this set of inequalities, we can split it into two parts, the

The first part, kx + b > 0, is to find the range of x corresponding to when the image of y = kx + b is above the x-axis.

In the second part, kx + b < mx, i.e., find the range of x corresponding to when the image of y = kx + b is below the image of y = mx.

Answer:

Example 5:

Analysis:

Answer:

Example 1:

Analysis:

First of all, the two functions of the system of simultaneous equations to find the coordinates of the intersection point, and then find the coordinates of the intersection point of the two functions and the x-axis, according to which the image is drawn, you can find the area of the triangle.

Answer:

Example 2:

Analysis:

Requirements BC, the first OA, then the two primary functions of the analytic formula, the value of x, y, can be derived from the coordinates of the A point. The use of the Pythagorean theorem can get the length of OA, so you can get the length of BC. By P (a, 0) can be seen, point B, point C horizontal coordinates and point P horizontal coordinates of the same, with an algebraic expression containing a B, C, the longitudinal coordinates of the vertical coordinates of the vertical coordinates of the absolute value of the subtraction, that is, the length of BC.

Answer: