Question

choose the transformations for the function as it compares to the parent function.
$f(x) = (x + 7)^3 - 5$
reflection: select
horizontal shift: select
horizontal shift by how many: select
vertical shift: select
vertical shift by how many: select

Explanation:

Step1: Identify parent function

Parent function is $g(x)=x^3$.

Step2: Check for reflection

No sign change on $x^3$ or $x$, so no reflection.

Step3: Analyze horizontal shift

For $f(x)=(x-h)^3+k$, $h=-7$, so shift left.
Horizontal shift: left, by 7 units.

Step4: Analyze vertical shift

$k=-5$, so shift downward.
Vertical shift: down, by 5 units.

Answer:

Reflection: No reflection
Horizontal shift: Left
Horizontal shift by how many: 7
Vertical shift: Down
Vertical shift by how many: 5