Write an equation for a function that has a graph with the given characteristics. The shape of y = 3 √ x shifted left 8 units and shifted up 3 units.

Answer 1

The original function is given by f(x) = 3√x.

To shift f 8 units to the left (horizontal shift):

f[x - (-8)] = f(x+8)

To shift that graph up 3 (vertical shift), add 3 outside the parentheses:

f(x+8) + 3

To write that as a function g(x), for example, picture substituting (x+8) into the f function:

3√( ) + 3

3 √(x+8) + 3

So, the transformed function is:

g(x) = 3√(x+8) + 3.

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