How to draw the image of function y = 1-1 / (x-1)

How to draw the image of function y = 1-1 / (x-1)

It can be converted into Y-1 = - 1 / (x-1), which is the inverse column function. The standard inverse column function y = 1 / X is realized by moving the image. The pithy formula: left plus right minus, up plus down minus

Draw an image of the function y = - 6 / X Only half a day

See the picture. You can do it by tracing points

Grade 1: how is the function image of y = | x-2|drawn? Focus on the process!

There are two cases
1. When x > or = 2, y = X-2, make the image, and the definition domain of the image is x > or = 2
2 when x

The solution of the equation x ^ 2 + √ 2x-1 = 0 can be regarded as the abscissa of the intersection point between the image of function y = x + √ 2 and the image of function y = 1 / X If x ^ 4 + ax-4 = 0, each real root x1, X2 The corresponding point (Xi, 4 / XI) (I = 1,2,...) corresponding to XK (K ≤ 4) If K) is on the same side of the line y = x, then the value range of real number a is? The answer is (- ∞, - 6) ∪ (6, + ∞) But it needs steps! It's better to be more detailed!

You must draw a picture of this problem, and then it will be clear at a glance
X ^ 4 + ax-4 = 0 move 4 to the right, obviously x = O is not the solution of the equation, so divide both sides of the equation by X to get x ^ 3-A = 4 / x, so the original equation is equivalent to finding the abscissa of the intersection point of x ^ 3-A and 4 / X
The point (x, 4 / x) is the intersection point of x ^ 3-A and 4 / X. it is better to find the intersection point of y = x and y = x / 4, which is a (- 2, - 2) and B (2,2). The abscissa of the intersection of x ^ 3 and 4 / X is positive or negative √ 2, that is, the left intersection is under a and the right intersection is on B. therefore, as long as the left intersection is on a after the x ^ 3 image is moved upward, the left and right intersection points are always on AB, that is, X (i.e. - 2) of point a is replaced by x ^ 3-A = 4 / X, So the absolute value of a is greater than 6, that is, A6
If it is not easy to understand, draw a picture to understand!

Is the symmetry center of the image of function y = cosx-2? Is the equation of symmetry axis?

The symmetry center of the image of function y = cosx-2 is (K π + π / 2, - 2) and the equation of symmetry axis is x = k π, K ∈ Z

The equation of an axis of symmetry of the function f (x) = (SiNx + cosx) 2 is () A. x=π Four B. x=π Three C. x=π Two D. x=π

∵f（x）=（sinx+cosx）2
=sin2x+2sinxcosx+cos2x
=1+sin2x，
From 2x = k π + π
2 (K ∈ z), x = k π
2+π
4（k∈Z），
Let k = 0, x = π
4，
The equation x = π for a symmetric axis of function f (x) = (SiNx + cosx) 2
4，
Therefore, a

The solution of the equation x squared plus the following sign 2x minus 1 = 0 can be regarded as the abscissa of the intersection point of the image of the function y = x plus the following sign 2 and the image of the function y = 1 / X The solution of the equation x squared plus the following sign 2x minus 1 = 0 can be regarded as the abscissa of the intersection point between the image of the function y = x plus the following sign 2 and the image of the function y = 1 / 1. If the points (Xi, 4 / XI) (I = 1,2,..., K) corresponding to the real numbers x1, X2,..., XK (k less than or equal to 4) of the equation x fourth power plus ax minus 4 = 0 are on the same side of the line y = x, then the value range of the real number a is?

The solution of the equation x ^ 4 + ax-4 = 0 can be regarded as the abscissa of the intersection point of the image of y = x ^ 3 + A and y = 4 / X. the image of y = 4 / X intersects with y = x at (- 2, - 2) and (2,2). When a > 0, (- 2) 3 + a > - 2, a > 6 is obtained

The function y = SiNx 2+ 3cosx An equation of symmetry axis for the image of 2 is () A. x=11 3 pi B. x=5π Three C. x＝−5π Three D. x＝−π Three

According to the sum difference formula, y = SiNx
2+
3cosx
2=2（ 1
2sinx
2+
Three
2cosx
2）=2sin（x
2+π
3），
The symmetry axis of y = SiNx is y = k π + 1
2π，k∈Z，
Let x
2+π
3=kπ+1
2π，
X = 2K π + π
3, and K ∈ Z
Obviously C is right
Therefore, C is selected

The image of y = cosx and y = - cosx are symmetric about ah

Even, this transformation is equivalent to flipping about the x-axis

What is the image of the function y = (e ^ x + e ^ - x) / (e ^ x-e ^ - x)?

If you want to simplify the formula, you can do it very well. The numerator and denominator are multiplied by e ^ X. (e ^ 2x + 1) / (e ^ 2x-1) = 1 + 2 / (e ^ 2x + 1). The graph can be drawn