Vertical shift up 5
Compare f(x)=x²+5 to the parent function. What happens?
A vertical shift is a transformation that moves the graph of a function up or down without changing its shape. We can apply a vertical shift up 5 to a function by adding 5 to the output or y-coordinate of each point on its graph.
For example, consider the function f(x) = x^2. To shift the graph of this function up 5 units, we can add 5 to the output of each point on its graph. The new function g(x) = f(x) + 5 is given by:
g(x) = x^2 + 5
The graph of g(x) will be identical to the graph of f(x), except that it will be shifted up 5 units. Each point on the original graph will be moved up by 5 units to create the new graph.
The general rule for a vertical shift up/down of h units is to replace f(x) with f(x) + h. For a vertical shift up, h is positive, and for a vertical shift down, h is negative.
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