Let's solve this problem step by step by setting the transformation a pattern function follows:
Step 1. Write the pattern function:
[tex]g(x)=x^3[/tex]
Step 2. Shift the graph 3 units to the left:
[tex]g(x)=(x+3)^3[/tex]
Step 3. Reflect the graph across the x-axis
[tex]g(x)=-(x+3)^3[/tex]
Step 4. Stretch the graph vertically by a factor of 2
[tex]g(x)=-2(x+3)^3[/tex]
Step 5. Shift the graph 1 unit up
[tex]g(x)=-2(x+3)^3+1[/tex]
