Question

Постройте график функции y=|x-3|+3

Answer 1

Graph of the Function y = |x - 3| + 3

To graph the function y = |x - 3| + 3, we can start by understanding the behavior of the absolute value function and then apply the necessary transformations.

The absolute value function |x| returns the distance of x from zero on the number line. It always returns a non-negative value. For example, |3| = 3 and |-3| = 3.

In the given function y = |x - 3| + 3, the expression (x - 3) inside the absolute value represents the distance of x from 3. Adding 3 to this distance gives us the final value of y.

Let's break down the graphing process into steps:

1. Find the vertex: - The vertex of the absolute value function y = |x| is at (0, 0). - In our case, the vertex of y = |x - 3| + 3 will be at (3, 3) because we are shifting the graph horizontally by 3 units to the right and vertically by 3 units up.

2. Determine the slope: - The slope of the absolute value function y = |x| is undefined because it has a sharp corner at the vertex. - Since we are not applying any additional transformations to the absolute value function, the slope of y = |x - 3| + 3 will also be undefined.

3. Plot additional points: - To graph the function, we can choose some x-values and calculate the corresponding y-values. - Let's choose x = 0, 1, 2, 3, 4, and 5 as our x-values and calculate the corresponding y-values using the equation y = |x - 3| + 3.

| x | y = |x - 3| + 3 | |---|----------------| | 0 | 6 | | 1 | 5 | | 2 | 4 | | 3 | 3 | | 4 | 4 | | 5 | 5 |

4. Plot the points and draw the graph: - Plot the points (0, 6), (1, 5), (2, 4), (3, 3), (4, 4), and (5, 5) on a coordinate plane. - Connect the points with a smooth curve.

The resulting graph of the function y = |x - 3| + 3 will be a V-shaped curve centered at (3, 3), opening upwards.


Please note that the graph provided is a visual representation and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate and precise graphs.