Understanding Vertical Translation in Mathematics: How to Shift a Graph or Function Up or Down Along the Y-axis

vertical translation

In mathematics, a vertical translation refers to shifting a graph or function vertically up or down along the y-axis

In mathematics, a vertical translation refers to shifting a graph or function vertically up or down along the y-axis. It involves adding or subtracting a constant value from the original function.

To perform a vertical translation, you need to understand the standard form of a function. The general form of a function equation is represented as:
y = f(x)

Let’s say you have the original function:
f(x) = x^2

To vertically translate this function, you’ll add or subtract a constant value to the original function, resulting in the translated function:
g(x) = f(x) + c

Here, “c” represents the constant value you will add or subtract to the original function.

If c > 0, the graph or function will be shifted vertically upwards. On the other hand, if c < 0, the graph or function will be shifted vertically downwards. For example, let's consider the original function f(x) = x^2. If we want to shift it 3 units upwards, we can write the translated function as: g(x) = f(x) + 3 Now let's plot the original and translated functions on a graph: Original function: f(x) = x^2 Translated function: g(x) = f(x) + 3 | (3,1) | (0,1) (3,0) -------|--------(0,0) | x-axis On the graph above, you can see that the original function f(x) = x^2 crosses the x-axis at point (0, 0) and y-axis at (0, 1). The translated function g(x) = f(x) + 3 has been shifted vertically upwards by 3 units, so it crosses the x-axis at (0, 3) and y-axis at (0, 4). Remember that a positive constant value c will shift the graph upwards, and a negative constant value c will shift the graph downwards.

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