The equation for the vertical translation of y=f(x). 4 units up is y=f(x)+4.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications/transformations to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)+4 are of the form (x,f(x)+4).
So, the graph for y=f(x) +4 is the same as the graph for y=f(x) shifted up by 4 units.
The new equation is:
y=f(x)+4
More problems related to the translation of shapes are given below.
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