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

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Answer 1 · 2016-11-29T01:41:30

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

Consider the parent graph $y = x^{3}$ $y=x^3$

The first transforamtion is 4 units left $\to$ $->$ replace $x$ $x$ with $(x + 4)$ $(x+4)$

The second transformation is 7 unit down $\to$ $->$ replace $y$ $y$ with $(y + 7)$ $(y+7)$

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

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

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

How do you write the equation for the graph obtained when the parent graph is y=x3y=x^3 and it is translated 4 unites left and 7 units down?