Question

y = \frac{1}{2}(x + 1)^4 - 3
describe the parent graph transformation
compression by 1/2, right 1, down 3
stretch by 1/2, right 1, down 3
stretch by 1/2, left 1, down 3
compression by 1/2, left 1, down 3

Explanation:

Step1: Identify parent function

Parent function is $y=x^4$

Step2: Analyze vertical transformation

The coefficient $\frac{1}{2}$ outside the power means a vertical compression by $\frac{1}{2}$.

Step3: Analyze horizontal shift

The $(x+1)$ term means a shift left by 1 unit.

Step4: Analyze vertical shift

The $-3$ at the end means a shift down by 3 units.

Answer:

compression by 1/2, left 1, down 3