Question

graph the function using a combination of transformations applied to the graph of a basic function.

\\g(x) = -4(x + 4)^3 - 2\\

Explanation:

Identify the parent function and transformations

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Determine key points on the transformed graph

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Answer:

To graph the function \(g(x) = -4(x+4)^3 - 2\), apply the following transformations to the parent cubic function \(f(x) = x^3\):

1. Horizontal Shift: Shift the graph 4 units to the left.
2. Vertical Stretch and Reflection: Stretch vertically by a factor of 4 and reflect across the \(x\)-axis.
3. Vertical Shift: Shift the graph 2 units down.

Key Points to Plot:

• Inflection point: \((-4, -2)\)
• Additional point 1: \((-3, -6)\)
• Additional point 2: \((-5, 2)\)