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.
Effect of the graph f(x) + 3
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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.
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.
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