Question

jordan is choose... the function h(x) can be written as choose..., which represents a vertical translation of g(x) choose... 3 units.

given the functions:
( g(x) = (x - 3)^3 )
( h(x) = (x - 3)^3 + 3 )

Explanation:

Step1: Recall Vertical Translation Rule

For a function \( y = f(x) \), the transformation \( y = f(x)+k \) is a vertical translation. If \( k>0 \), it's a shift up; if \( k < 0 \), it's a shift down.
Here, \( g(x)=(x - 3)^3 \) and \( h(x)=(x - 3)^3+3 \). So \( h(x)=g(x)+3 \).

Step2: Analyze the Transformation

Comparing \( h(x) \) and \( g(x) \), we see that \( h(x) \) is obtained by adding 3 to \( g(x) \). By the vertical translation rule, adding a positive constant to the function shifts the graph up. So \( h(x) \) is \( g(x) \) shifted up 3 units.

Answer:

• Jordan is (assuming context about recognizing vertical translation, so the first "Choose..." should relate to identifying vertical translation, then \( h(x)=g(x)+3 \), and the vertical translation is up 3 units. So filling the blanks: The first "Choose..." (about what Jordan is doing, likely recognizing transformation) → recognizing vertical translation; \( h(x) \) can be written as \( g(x)+3 \); vertical translation of \( g(x) \) up 3 units.