Question

describe the transformations and select the appropriate parent function.
select all that apply.
$y = -(x + 1)^3 - 3$
$square$ shifts up 3
$square$ shifts down 3
$square$ shifts left 1
$square$ shifts right 1
$square$ vertically stretches by a factor of 2
$square$ vertically compresses by a factor of 1/2
$square$ reflects over the x-axis
$square$ cubic function
$square$ cube root function

Explanation:

1. The parent function of $y=-(x+1)^3-3$ is the cubic function $y=x^3$.
2. The $-3$ outside the cube shifts the parent function down 3 units.
3. The $+1$ inside the cube with $x$ shifts the parent function left 1 unit.
4. the negative sign in front of the cube reflects the parent function over the x-axis.
5. The function is a transformed cubic function, so "Cubic Function" is the correct parent function classification.

Answer:

• Shifts down 3
• Shifts left 1
• Reflects over the x-axis
• Cubic Function