Reflect Stretch Db40Eb

1. **State the problem:** We need to find the function that results from reflecting the graph of $y=x^3$ through the x-axis and then stretching it vertically by a factor of 2. 2. **Reflection through the x-axis:** Reflecting a function $y=f(x)$ through the x-axis changes the sign of the output, so the reflected function is $y=-f(x)$. 3. **Vertical stretch by a factor of 2:** Stretching a function vertically by a factor of 2 multiplies the output by 2, so the stretched function is $y=2f(x)$. 4. **Apply reflection first:** Reflect $y=x^3$ through the x-axis: $$y = -x^3$$ 5. **Apply vertical stretch:** Stretch the reflected function by a factor of 2: $$y = 2(-x^3) = -2x^3$$ 6. **Final function:** The function after reflection and vertical stretch is: $$y = -2x^3$$ This function reflects the original cubic graph through the x-axis and stretches it vertically by 2.