Answer :
To describe the transformation from the parent absolute value function [tex]\( y = |x| \)[/tex] to the function [tex]\( y = |x| - 5 \)[/tex], follow these steps:
1. Understand the Parent Function:
The parent function is [tex]\( y = |x| \)[/tex]. The graph of this function is a V-shaped graph that opens upward with its vertex at the origin (0, 0).
2. Identify the Transformation:
The transformation involves the term [tex]\(-5\)[/tex] which is outside the absolute value function.
3. Determine the Type of Transformation:
In the given function [tex]\( y = |x| - 5 \)[/tex], the [tex]\(-5\)[/tex] is subtracted from the absolute value. A transformation of the form [tex]\( y = |x| + k \)[/tex] or [tex]\( y = |x| - k \)[/tex] corresponds to a vertical shift.
- When [tex]\( k \)[/tex] is positive ([tex]\( y = |x| + k \)[/tex]), the graph shifts upward by [tex]\( k \)[/tex] units.
- When [tex]\( k \)[/tex] is negative ([tex]\( y = |x| - k \)[/tex]), the graph shifts downward by [tex]\( k \)[/tex] units.
4. Apply the Transformation:
Here, [tex]\( k = -5 \)[/tex]. Since [tex]\( k \)[/tex] is negative, this means the graph of the parent function [tex]\( y = |x| \)[/tex] will shift downward by 5 units.
Therefore, the transformation from the parent absolute value function [tex]\( y = |x| \)[/tex] to [tex]\( y = |x| - 5 \)[/tex] is a shift down 5 units.
Hence, the answer is:
1. Shift down 5 units
1. Understand the Parent Function:
The parent function is [tex]\( y = |x| \)[/tex]. The graph of this function is a V-shaped graph that opens upward with its vertex at the origin (0, 0).
2. Identify the Transformation:
The transformation involves the term [tex]\(-5\)[/tex] which is outside the absolute value function.
3. Determine the Type of Transformation:
In the given function [tex]\( y = |x| - 5 \)[/tex], the [tex]\(-5\)[/tex] is subtracted from the absolute value. A transformation of the form [tex]\( y = |x| + k \)[/tex] or [tex]\( y = |x| - k \)[/tex] corresponds to a vertical shift.
- When [tex]\( k \)[/tex] is positive ([tex]\( y = |x| + k \)[/tex]), the graph shifts upward by [tex]\( k \)[/tex] units.
- When [tex]\( k \)[/tex] is negative ([tex]\( y = |x| - k \)[/tex]), the graph shifts downward by [tex]\( k \)[/tex] units.
4. Apply the Transformation:
Here, [tex]\( k = -5 \)[/tex]. Since [tex]\( k \)[/tex] is negative, this means the graph of the parent function [tex]\( y = |x| \)[/tex] will shift downward by 5 units.
Therefore, the transformation from the parent absolute value function [tex]\( y = |x| \)[/tex] to [tex]\( y = |x| - 5 \)[/tex] is a shift down 5 units.
Hence, the answer is:
1. Shift down 5 units
