Which equation defines the graph of y = x³ 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 = x³ is shifted vertically 5 units down and horizontally left 4 units.

If the function y = x³ is shifted vertically 5 units down it transforms itself into the following equation:

y = x³ - 5

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

If the function y = x³ 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 = x³ after it is shifted vertically 5 units down and horizontally left 4 units

Summary:

The equation defines the graph of y = x³ after it is shifted vertically 5 units down and horizontally left 4 units is y = (x - 4)³ - 5