Question

choose all correct answers that describe the transformation from the parent graph to the new graph. (chapter 2)
there is 1 answer for this question!
$f(x) = x^2$ ; $g(x) = x^2 - 11$
\bigcirc 11 to the right
\bigcirc 11 to the left
\bigcirc 11 down
\bigcirc 11 up

Explanation:

Step1: Recall Vertical Shift Rule

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

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

Here, \( f(x)=x^2 \) and \( g(x)=x^2 - 11 \), which can be written as \( g(x)=f(x)-11 \). Comparing with \( y = f(x)+k \), \( k = - 11 \) (negative), so it's a vertical shift down by 11 units.

Answer:

11 down