Question

Функцію задано формулою у = 0,2x - 0,8. Не виконуючи побудови: a) знайдіть нулі функції; б) з'ясуйте, чи проходить графік функції через точку A(9, 1). З РОЗВ'ЯЗАННЯМ

Answer 1

у=0,2х-0,8

а)

0,2х-0,8=0

0,2х=0,8

х=0,8:0,2

х=4 - нуль функции

б)

Если график функции проходит через заданную точку, то выражения справа должно быть равно левой части:

А(9;1) =>х=9; у=1

1=0,2•9-0,8

1=1,8-0,8

1=1

Ответ:а)х=4;б) проходит

Answer 2

Function and its zeros

The given function is defined by the formula u = 0.2x - 0.8. We are asked to find the zeros of the function.

To find the zeros of a function, we need to solve the equation u = 0. By substituting the given formula into the equation, we get:

0.2x - 0.8 = 0

To solve this equation, we can add 0.8 to both sides and then divide both sides by 0.2:

0.2x = 0.8 x = 0.8 / 0.2 x = 4

Therefore, the zero of the function is x = 4.

Graph of the function and point A(9, 1)

We are also asked to determine whether the graph of the function passes through the point A(9, 1).

To check if a point lies on the graph of a function, we need to substitute the coordinates of the point into the equation of the function and see if the equation holds true.

Substituting x = 9 and u = 1 into the equation u = 0.2x - 0.8, we get:

1 = 0.2 * 9 - 0.8 1 = 1.8 - 0.8 1 = 1

Since the equation holds true, we can conclude that the graph of the function passes through the point A(9, 1).