Question

Постройте график функции y=1-|x-2|

Answer 1

Вот. приложение- MalMath, оно бесплатное.

Answer 2

Graph of the Function y=1-|x-2|

To graph the function \(y=1-|x-2|\), we can start by understanding the basic shape of the absolute value function and then apply the necessary transformations.

The absolute value function \(y=|x|\) has a V-shaped graph with its vertex at the origin (0, 0). When we introduce a horizontal shift of 2 units to the right, the graph of \(y=|x-2|\) will shift 2 units to the right. The negative sign in front of the absolute value reflects the graph over the x-axis.

Let's plot the points and graph the function.

Plotting the Points

We can start by finding the key points of the function: - When \(x=0\), \(y=1-|0-2|=3\) - When \(x=1\), \(y=1-|1-2|=0\) - When \(x=2\), \(y=1-|2-2|=1\) - When \(x=3\), \(y=1-|3-2|=0\)

Graphing the Function

Now, let's plot these points and draw the graph of the function \(y=1-|x-2|\).

The graph of the function \(y=1-|x-2|\) will have a V-shaped graph shifted 2 units to the right and reflected over the x-axis.

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