1. **State the problem:** We need to graph the function $$y = 3\sqrt[3]{x} - 5$$ by transforming the parent function $$y = \sqrt[3]{x}$$. 2. **Parent function and transformations:** The parent function is $$y = \sqrt[3]{x}$$, which has a characteristic S-shaped curve passing through the origin (0,0). 3. **Transformations applied:** - The coefficient 3 in front of the cube root stretches the graph vertically by a factor of 3. - The minus 5 shifts the graph downward by 5 units. 4. **Formula for transformations:** If the parent function is $$f(x) = \sqrt[3]{x}$$, then the transformed function is $$g(x) = a f(x) + k$$ where $$a=3$$ (vertical stretch) and $$k=-5$$ (vertical shift). 5. **Calculate key points:** - At $$x = -8$$: $$y = 3 \sqrt[3]{-8} - 5 = 3(-2) - 5 = -6 - 5 = -11$$ - At $$x = -1$$: $$y = 3 \sqrt[3]{-1} - 5 = 3(-1) - 5 = -3 - 5 = -8$$ - At $$x = 0$$: $$y = 3 \sqrt[3]{0} - 5 = 0 - 5 = -5$$ - At $$x = 3$$: $$y = 3 \sqrt[3]{3} - 5 = 3(\sqrt[3]{3}) - 5$$ (approx. $$3(1.442) - 5 = 4.326 - 5 = -0.674$$) - At $$x = 7$$: $$y = 3 \sqrt[3]{7} - 5 = 3(\sqrt[3]{7}) - 5$$ (approx. $$3(1.913) - 5 = 5.739 - 5 = 0.739$$) 6. **Summary:** The graph is the cube root curve vertically stretched by 3 and shifted down by 5 units. It passes through points approximately (-8,-11), (-1,-8), (0,-5), (3,-0.674), and (7,0.739). 7. **Final answer:** The transformed graph of $$y = 3\sqrt[3]{x} - 5$$ is the parent cube root graph stretched vertically by 3 and shifted down 5 units.