To analyze how the vertical shift affects the parent function (which is typically taken to be \( y = x \) for linear functions), let’s look at a transformation.
The equation \( y = x + 5 \) is a transformation of the parent function \( y = x \). In general, when we talk about shifting a function vertically, we're looking at how adding or subtracting a constant affects the graph of the function.
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Vertical Shift: The "+5" in \( y = x + 5 \) indicates that the graph of the parent function \( y = x \) is shifted upward by 5 units. This means that every point on the graph of the parent function will be raised by 5 units.
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Effect on Points: For example, if we take a point on the parent function such as (0, 0), after the transformation, it will move to (0, 5). Similarly, if there was a point (1, 1) on the parent function, it will shift to (1, 6).
In conclusion, the statement that best describes how the vertical shift affects the parent function is:
"The graph of the parent function y = x is shifted upward by 5 units."