Question

Transformation g(x)=-2(x+3)^3+1

Answer 1

Explanation:

Let's solve this problem step by step by setting the transformation a pattern function follows:

Step 1. Write the pattern function:

$g(x)=x^3$

Step 2. Shift the graph 3 units to the left:

$g(x)=(x+3)^3$

Step 3. Reflect the graph across the x-axis

$g(x)=-(x+3)^3$

Step 4. Stretch the graph vertically by a factor of 2

$g(x)=-2(x+3)^3$

Step 5. Shift the graph 1 unit up

$g(x)=-2(x+3)^3+1$