Effect of the graph f(x) + 3
The effect of adding 3 to the graph of f(x) can be seen as a vertical shift upwards by 3 units. In other words, every point on the original graph is moved 3 units higher on the y-axis.
Mathematically, if (x, y) is a point on the graph of f(x), then the corresponding point on the graph of f(x) + 3 would be (x, y + 3).
This shift does not change the shape or the direction of the graph. Any increasing or decreasing trends in the original graph will still be present in the shifted graph. The main difference is that all the y-values of the shifted graph will be 3 units higher than the y-values of the original graph.
in equation form?
In equation form, if the original graph is represented by f(x), then the graph of f(x) + 3 can be written as:
y = f(x) + 3
where y represents the new shifted y-values and f(x) represents the y-values of the original graph. This equation indicates that for every x-value, the corresponding y-value on the shifted graph is obtained by adding 3 to the original y-value.
To understand the effect of the graph f(x) + 3, we need to examine how each point on the graph is transformed.
Adding 3 to the function f(x) can be thought of as vertically shifting the graph of f(x) upward by 3 units. This means that every point on the original graph will be moved vertically upward by 3 units.
If a point (x, y) is on the original graph f(x), then the corresponding point on the graph of f(x) + 3 will have the coordinates (x, y + 3). This transformation will be applied to every point on the graph of f(x), resulting in a new graph that is shifted upward by 3 units.
In summary, adding 3 to the function f(x) causes a vertical shift of the graph upward by 3 units.
To determine the effect of adding 3 to a graph, such as f(x), we need to understand how it changes the y-values or the vertical position of the points on the graph.
First, let's consider the original graph of f(x). If there are specific points on the graph that are given, we can find their corresponding y-values. If the graph is given without specific points, we can imagine any arbitrary point and follow the same process.
1. Choose a point on the original graph, let's call it (x, y₀).
2. Add 3 to the y-coordinate of the chosen point:
newY = y₀ + 3
3. The new point will be (x, newY) on the modified graph.
By adding 3 to the y-values of each point on the original graph, we shift the entire graph vertically upward by 3 units. This means that every point on the modified graph will have a y-coordinate that is 3 units greater than its corresponding point on the original graph.
In summary, the effect of the graph f(x) + 3 is a vertical shift upward by 3 units.