Question

как строить график функции |x-2|-y=6

Answer 1

Ну во-первых преобразовать |x-2|-y=6 в y=|x-2|-6 
А во-вторых строится как график модуля, но со сдвигом на 2 единицы вправо и на 6 вниз-все на рисунке

Answer 2

Building the Graph of the Function |x-2|-y=6

To build the graph of the function |x-2|-y=6, we need to understand the equation and plot the points that satisfy it.

The equation |x-2|-y=6 represents a function with an absolute value. To graph this function, we can break it down into two cases: when x-2 is positive and when x-2 is negative.

Case 1: x-2 is positive When x-2 is positive, the equation becomes x-2-y=6. We can rewrite this as y = x-8.

Case 2: x-2 is negative When x-2 is negative, the equation becomes -(x-2)-y=6. Simplifying this, we get -x+2-y=6. We can rewrite this as y = -x-4.

Now, let's plot the points that satisfy these two cases.

For Case 1, when x-2 is positive: - Let's choose some x-values and calculate the corresponding y-values using the equation y = x-8. - For example, when x = 0, y = 0-8 = -8. So, one point is (0, -8). - Similarly, when x = 4, y = 4-8 = -4. So, another point is (4, -4).

For Case 2, when x-2 is negative: - Let's choose some x-values and calculate the corresponding y-values using the equation y = -x-4. - For example, when x = -2, y = -(-2)-4 = 2-4 = -2. So, one point is (-2, -2). - Similarly, when x = -6, y = -(-6)-4 = 6-4 = 2. So, another point is (-6, 2).

Now, let's plot these points on a graph and connect them to visualize the function.

Graph of the function |x-2|-y=6:

   y
   |
   |
   |        * (-6, 2)
   |
   |
   |    * (0, -8)
   |
   |_____________________
            x

In the graph above, the points (-6, 2) and (0, -8) represent the solutions to the equation |x-2|-y=6. The graph consists of two line segments, one with a positive slope (y = x-8) and the other with a negative slope (y = -x-4). The two line segments intersect at the point (2, -6), which is the vertex of the absolute value function.

Please note that the graph provided is a rough sketch and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate representations of functions.

I hope this helps! Let me know if you have any further questions.