What is the equation of the graph obtained when the parent graph y=x^3 translated 4 units left and 7 units down?

Parent function describes the general formula of a graph without a translation, or shift of any kind. When considering how these shifts affect the graph, a translation to the left or right would affect the x-axis and a translation up or down would affect the y-axis. When the x-axis is affected, that constant must be connected to the variable 'x', while a movement up or down must be separated and connected to the variable 'y'. In the case of the parent function y = x³, adding '4' to the variable 'x' would shift the graph left and subtracting the '7' as a constant of the expression would move the graph down:

y = (x + 4)³ - 7

BladeRunner212 BladeRunner212 · Answer 2 · 2019-10-18T14:26:07+02:00

y = (x + 4)³ - 7

Further explanation

There are four types of transformation geometry:

translation (or shifting),
reflection,
rotation, and
dilation (stretching or shrinking).

In this case, the transformation is shifting vertically and horizontally.

Translation (or shifting): moving a graph on an analytic plane without changing its shape.
Vertical shift: moving a graph upwards or downwards without changing its shape.
Horizontal shift: moving a graph to the left or right downwards without changing its shape.

Vertical Shift

Given the graph of y = f(x) and v > 0, we obtain the graph of:

[tex]\boxed{ \ y = f(x) + v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward v units.
[tex]\boxed{ \ y = f(x) - v \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] downward v units.

Horizontal Shift

Given the graph of y = f(x) and h > 0, we obtain the graph of:

[tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.
[tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.