Question

the function $k(x) = |x + 3| + 3$, is translated 3 units select choice and 3 units select choice in relation to the parent function.

Explanation:

Step1: Recall Parent Function

The parent function of absolute value is \( y = |x| \). Its vertex is at \( (0,0) \).

Step2: Analyze Horizontal Translation

For a function \( y = |x - h| + k \), the horizontal translation is determined by \( h \). In \( k(x)=|x + 3|+3 \), we can rewrite \( x + 3 \) as \( x-(-3) \). So, \( h=-3 \). A negative \( h \) means the graph is translated \( |h| \) units to the left. So, horizontal translation: 3 units left.

Step3: Analyze Vertical Translation

The vertical translation is determined by \( k \). In \( k(x)=|x + 3|+3 \), \( k = 3 \). A positive \( k \) means the graph is translated \( k \) units up. So, vertical translation: 3 units up.

Answer:

First "Select Choice": left; Second "Select Choice": up