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y = (x + 4)³ - 7
<h3>Further explanation </h3>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:
by shifting the graph of
upward v units.
by shifting the graph of
Horizontal Shift
Given the graph of y = f(x) and h > 0, we obtain the graph of:
by shifting the graph of
by shifting the graph of
- - - - - - - - - -
<u>Given:</u>
The parent graph
<u>Question:</u>
What is the equation of the graph obtained when the parent graph y=x^3 translated 4 units left and 7 units down?
<u>The Process:</u>
Clearly, we must translate the graph of to obtain the new equation of the graph.
translated 4 units left.
It becomes
Furthermore, translated 7 units down.
Thus, the result is
<u>Conclusion </u>
Thus, when the parent graph of y = x³ translated 4 units left and 7 units down, the result is the equation of the graph y = (x + 4) ³ - 7
<h3>Learn more </h3>- Transformations that change the graph of f(x) to the graph of g(x) brainly.com/question/2415963
- The similar problem brainly.com/question/1369568
- Which equation represents the new graph brainly.com/question/2527724
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