Asked by Nevaeh Rolen
Identify the transformations for the following function y=|x+4|-3
HS 4 to the right, VS down 3
HS 4 to the left, VS down 3
HS 3 to the right, VS up 4
HS 3 to the left. VS up 4
HS 4 to the right, VS down 3
HS 4 to the left, VS down 3
HS 3 to the right, VS up 4
HS 3 to the left. VS up 4
Answers
Answered by
GPT-4o mini
To analyze the function \( y = |x + 4| - 3 \), we can break it down into its transformations from the parent function \( y = |x| \).
1. **Horizontal Shift (HS)**: The term \( (x + 4) \) indicates a horizontal shift. The general form for horizontal shifts is \( y = |x - h| \), where \( h \) is the amount of the shift. In this case, since we have \( x + 4 \), it corresponds to \( x - (-4) \), which means it shifts **4 units to the left**.
2. **Vertical Shift (VS)**: The term \( -3 \) indicates a vertical shift. The function \( |x| - k \) shifts the graph down by \( k \). Here, \( -3 \) shifts the graph **down 3 units**.
Putting this together, the function \( y = |x + 4| - 3 \) represents a horizontal shift 4 units to the left and a vertical shift down 3 units.
Thus, the correct option is:
**HS 4 to the left, VS down 3**.
1. **Horizontal Shift (HS)**: The term \( (x + 4) \) indicates a horizontal shift. The general form for horizontal shifts is \( y = |x - h| \), where \( h \) is the amount of the shift. In this case, since we have \( x + 4 \), it corresponds to \( x - (-4) \), which means it shifts **4 units to the left**.
2. **Vertical Shift (VS)**: The term \( -3 \) indicates a vertical shift. The function \( |x| - k \) shifts the graph down by \( k \). Here, \( -3 \) shifts the graph **down 3 units**.
Putting this together, the function \( y = |x + 4| - 3 \) represents a horizontal shift 4 units to the left and a vertical shift down 3 units.
Thus, the correct option is:
**HS 4 to the left, VS down 3**.