Question

shifting the cubic function practice
complete this assessment to review what youve learned. it will not count toward your grade.
given the function $f(x) = x^3$, how many units and in what direction will the graph of $g(x) = f(x) - 3$ be shifted?
option #1: the graph will shift vertically 3 units down.
option #2: the graph will shift vertically 3 units up.
option #3: the graph will shift horizontally 3 units to the left.
(1 point)
the best answer to the question is option #\square.

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = f(x) + k \), if \( k>0 \), shift up \( k \) units; if \( k<0 \), shift down \( |k| \) units.
Here, \( g(x)=f(x)-3=f(x)+(-3) \), so \( k = - 3 \).

Step2: Determine Shift Direction and Units

Since \( k=-3<0 \), the graph of \( g(x) \) is the graph of \( f(x) \) shifted vertically down by \( | - 3|=3 \) units.

Answer:

Option #1. The graph will shift vertically 3 units down