Question

Постройте график функции у=х-5С помощью графика найдитеа) Наибольшее и наименьшее значение функции на отрезке [0;3]б)значение переменной х, при которых у=0, у>0

Answer 1

Очень легкое задание ,если не полениться и НАРИСОВАТЬ ГРАФИК у=х-5

Там в Б)(последнее) X>5

Answer 2

Graph of the Function y = x - 5

To plot the graph of the function \( y = x - 5 \), we can use the given equation to find the corresponding y-values for different x-values. Then, we can plot these points on a graph to visualize the function.

Let's start by finding the y-values for the x-values in the interval [0, 3].

- For x = 0: \( y = 0 - 5 = -5 \) - For x = 1: \( y = 1 - 5 = -4 \) - For x = 2: \( y = 2 - 5 = -3 \) - For x = 3: \( y = 3 - 5 = -2 \)

Now, let's plot these points on a graph.

The graph of the function \( y = x - 5 \) is a straight line with a slope of 1 and y-intercept of -5.

Analysis of the Graph

a) Maximum and Minimum Values on the Interval [0, 3]

To find the maximum and minimum values of the function on the interval [0, 3], we need to examine the graph within this interval.

From the graph, we can see that the function is a straight line with a negative slope. Since the slope is positive, the function increases as x increases. Therefore, the minimum value occurs at the left endpoint of the interval (x = 0), and the maximum value occurs at the right endpoint of the interval (x = 3).

b) Values of x for y = 0 and y > 0

To find the values of x for which y = 0, we need to solve the equation \( x - 5 = 0 \). This gives us \( x = 5 \).

For y > 0, we need to find the x-values for which the function \( y = x - 5 \) is greater than 0. Since the function is a straight line with a positive slope, it is greater than 0 for all x-values greater than 5.

Therefore, the value of x when y = 0 is 5, and the values of x for which y > 0 are all x-values greater than 5.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.