Transformations and functions: vertical shift

The graph of a function y = f(x) is vertically shifted H units up when you add H to the function.

For example, if f(x) = x^{2} and g(x) = x^{2} + 1, then the graph of g(x) is the same as the graph of f(x), shifted up one unit.

Rewrite the following functions with the indicated shift. Check the graphs with a graphing program such as desmos.com:

1. Shift up 2 units: f(x) = 2x – 4

2. Shift down 3 units: f(x) = 4x^{3}

3. Shift up 10 units: f(x) = sqrt(x) (f(x) = square root of x).

4. Shift up 5 units: f(x) = 1/x

5. Shift down 100 units: f(x) = x^{1.5}

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