High school all function image

2. For hyperbola y = K / x, if any real number is added to or subtracted from the denominator (i.e. y = K / (...). 2

High school function image
Given the function f (x) = | - x ^ 2 + 3x-2 |, try to make this function image
How to draw this kind of picture···

This method of adding absolute value to the whole function is to symmetrically fold the image below the X axis to the image above the X axis

The drawing method of function image for y = (5x-1) / (x + 2), except for tracing point

The function expressions are sorted out
y=(5x-1)/(x+2)=[5(x+2)-11]/(x+2)=5-11/(x+2)
That is y = - 11 / (x + 2) + 5
Drawing:
① Draw an image of y = 11 / X
② Add left and subtract right, and move the image two unit lengths to the left to get the image of y = 11 / (x + 2)
③ Add a minus sign, symmetrical about the X axis
④ Constant + 5, all move up 5 units

Making the function image of y = 2Sin (3x + π / 5) - 1 by five point method

Find the tangent equation of the image with function y = 1 / X at point (2,1 / 2)

Take the derivative y '= - 1 / x ^ 2 first
That is, tangent slope k = - 1 / 4
Point oblique: Y-1 / 2 = - 1 / 4 (X-2)
The tangent equation is y = - 1 / 4x + 1

How to find tangent equation of function

Let P (x0, Y0)
Tangent of function y = f (x) through p
Let the tangent point be (x, f (x))
From the slope relation
f'(x)=(f(x)-y0)/((x-x0)
We can get X
Solving tangent equation again

Given the function y = xlnx, find its tangent equation at point x = 1

When ∵ y = xlnx, ∵ y ′ = 1 × LNX + X · 1x = 1 + LNX, ∵ x = 1, y ′ = 1. When x = 1, y = 0, ∵ the tangent equation at point x = 1 is y = X-1

How to find the tangent equation at a certain point of a function or the tangent equation at x = a

1. Derivation function
2. Let the tangent point be f '(k)
3. Y-m = f '(k) * (x-n) with known points
4. Find f '(k)
5. Make the equation into general form

A tangent method for finding the zero point of a function

You're talking about the Newton Raphson method
The key is the iteration formula
x(n+1)=x(n)-f(x(n))/f'(x(n))

High school all function image