# Which equation defines the graph of y = x^{3} after it is shifted vertically 5 units down and horizontally left 4 units

y = (x - 4)^{3} - 5

y = (x + 5)^{3} - 4

y = (x + 5)^{3} + 4

y = (x + 4)^{3} - 5

**Solution:**

We need to find the transformation undergone when the graph of y = x^{3} is shifted vertically 5 units down and horizontally left 4 units.

If the function y = x^{3} is shifted vertically 5 units down it transforms itself into the following equation:

y = x^{3} - 5

For every value of x the y value is decreased by 5.

If the function y = x^{3} is shifted horizontally left then it implies that the x value is decreased .

Since in the given problem the functions shifts left by 4 units we have:

y = (x - 4)^{3}

Now combining both the actions we get the the final transformed equation as :

y = (x - 4)^{3} - 5

## Which equation defines the graph of y = x^{3} after it is shifted vertically 5 units down and horizontally left 4 units

**Summary:**

The equation defines the graph of y = x^{3} after it is shifted vertically 5 units down and horizontally left 4 units is y = (x - 4)^{3} - 5

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