Using translation concepts, the graph of f(x) = (x + 7)³-8 comparing to the parent function g(x) = x³ is:
Shifted 7 units to the left.
Shifted 8 units down.
<h3>Define translations.</h3>
A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Given,
Function
f(x) = (x+7)³ + 8
Parent function,
g(x) = x³
Since we know that, the graph is moved 8 units to the left. Finding g(x+ a) translation to moving the graph a unit to the right.
In this function, 8 is subtracted, hence the graph was also shifted 4 units higher. Subtracting a to the function is equivalent to moving the graph down a unit.
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