graph the equation by tanslationg y=[x]
y=[x+7]
To graph the equation y = [x+7], we can start by understanding the effect of the equation on the basic graph of y = [x].
The equation y = [x+7] shifts the graph of y = [x] to the left by 7 units.
Here's how you can graph the equation:
1. Plot a few key points on the graph of y = [x]. Since the basic graph of y = [x] is the floor function, it consists of a series of points where y is an integer and x can be any real number.
For example:
- When x = -3, y = [-3] = -3.
- When x = -1.5, y = [-1.5] = -2.
- When x = 0, y = [0] = 0.
- When x = 1.2, y = [1.2] = 1.
- When x = 4, y = [4] = 4.
2. Translate each of these points 7 units to the left. For example, the point (-3, -3) will now become (-3-7, -3) = (-10, -3). Similarly, the point (1.2, 1) will become (1.2-7, 1) = (-5.8, 1).
3. Connect the translated points with straight lines. Since the graph consists of discrete points, you can connect them using line segments or dots.
The resulting graph will be a shifted version of the basic graph y = [x] to the left by 7 units.
Note: The square brackets notation [x] represents the floor function, which rounds down x to the nearest integer.