Given the function f (x) = x + m, and the function image passes through the point (1,5), then the value of real number m is

Given the function f (x) = x + m, and the function image passes through the point (1,5), then the value of real number m is

Just substitute the point in the equation, M = 4
We should know the meaning of the combination of number and shape

(good Bonus) given the function y = (m-1) x ^ 2 + (M-3) x + (m-1), when m is a real number, the function image and x-axis
1. There is no common point
2. There is only one common point
3. There are two different common points

If M = 1, the function is y = - 2x and has a common point with X axis
If M ≠ 1, the function is quadratic
Discriminant △ = (M-3) & sup2; - 4 (m-1) & sup2; = - 3M & sup2; + 2m + 5 = (- 3M + 1) (M + 5)
If there is no common point between function image and x-axis
Then △ 0, that is (- 3M + 1) (M + 5) ＜ 0
The solution is m ＞ 1 / 3 or m ＜ - 5, and m ≠ 1
If there is only one common point between function image and x-axis
Then △ = 0, that is (- 3M + 1) (M + 5) = 0
The solution is m = 1 / 3 or - 5
If the function image and X axis have two different common points
Then △ 0, that is (- 3M + 1) (M + 5) > 0
The solution is - 5 < m < 1 / 3
To sum up
If M ＞ 1 / 3 or m ＜ - 5 and m ≠ 1, there is no common point between the function image and x-axis
When m = 1 / 3 or M = - 5 or M = 1, there is only one common point between the function image and the x-axis
When - 5 < m < 1 / 3, the function image and X-axis have two different common points

If the function f (x) defined on R is an odd function with a period of 2, then the equation f (x) = 0 has at least several real roots on [- 2,2]? Why are there five not three? Why do F, (1) and f (- 1) also count?

F (1) = - f (- 1) [odd function]
F (- 1 + 2) = f (- 1), that is, f (1) = f (- 1) [periodicity]
We get f (1) = f (- 1) = 0
So the five points of - 2, - 1,0,1,2 f (x) = 0