Question: Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting…

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting.

\[ h(x) = -x^3 - 9 \]

Use the graphing tool to graph the function.

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Solution

To graph the function \( h(x) = -x^3 - 9 \) using the techniques of shifting, compressing, stretching, and/or reflecting, let’s analyze it step by step. 1. Identify the base function: The base function is \( f(x) = x^3 \). 2. Reflect over the x-axis: The negative sign in front of the base function indicates a reflection over the x-axis. Thus, we have: \[ g(x) = -x^3 \] 3. Shift downward: The term \(-9\) indicates a vertical shift downward by 9 units. Therefore, the transformed function is: \[ h(x) = -x^3 - 9 \] Now, to graph \( h(x) \), start by sketching the graph of \( f(x) = x^3 \), then: - Reflect it over the x-axis to get \( g(x) = -x^3 \). - Finally, shift the resulting graph downward by 9 units to get \( h(x) = -x^3 - 9 \).