Question

the function $f(x) = x^3 - 7$ is the function $g(x) = x^3$ shifted vertically downward. how many units downward was $g(x)$ shifted vertically to obtain $f(x)$? (1 point)
○ 6
○ 8
○ 4
○ 7

Explanation:

Step1: Recall Vertical Shift Rule

For a function \( y = g(x) + k \), if \( k>0 \), it's a vertical shift up by \( k \) units; if \( k<0 \), it's a vertical shift down by \( |k| \) units.

Step2: Analyze \( f(x) \) and \( g(x) \)

Given \( g(x)=x^3 \) and \( f(x)=x^3 - 7 \). Comparing with \( y = g(x)+k \), here \( k=-7 \).

Step3: Determine Shift Units

The absolute value of \( k \) is \( | - 7|=7 \), so \( g(x) \) is shifted downward by 7 units to get \( f(x) \).

Answer:

7 (corresponding to the option with 7, assuming the last option is 7: "7")