Question

How do you write the equation for the graph obtained when the parent graph is `y=x^3` and it is translated 4 unites left and 7 units down?

Answer 1

The equation of the transformed graph would be: `y+7 = (x+4)^3`

Explanation:

Consider the parent graph `y=x^3`

The first transforamtion is 4 units left `->` replace `x` with `(x+4)`

The second transformation is 7 unit down `->` replace `y` with `(y+7)`

Hence: The equation of the transformed graph would be: `y+7 = (x+4)^3`

The graph of the transformed `y` is shown below:

graph{(x+4)^3-7 [-25.66, 25.66, -12.83, 12.82]}