Transformation of Functions
The equation provided suggests a transformation of the base function \( f(x) \) applied to produce the new function \( y \). The transformation can be described as follows:
1. Horizontal shift: The expression \( (x - 5) \) indicates that the graph of \( f(x) \) is shifted to the right by 5 units. Therefore, \( B = 5 \) (right).
2. Vertical shift: The \( +8 \) at the end of the function indicates that the graph is shifted upwards by 8 units. So, \( D = 8 \) (up).
There is no indication in the equation of a horizontal stretch/shrink or reflection (which would be indicated by a multiplier in front of the \( x \) term inside the function), nor is there a vertical stretch/shrink or reflection (which would be indicated by a coefficient in front of the \( f(x) \) term). Thus, we can assume no changes have been made in these aspects. Consequently, \( A \) (representing horizontal stretch/shrink and reflection) and \( C \) (representing vertical stretch/shrink and reflection) remain unchanged:
3. \( A = 1 \) (no horizontal stretch/shrink or reflection).
4. \( C = 1 \) (no vertical stretch/shrink or reflection).
Transformations:
- A horizontal shift to the right by 5 units.
- A vertical shift upwards by 8 units.
- No horizontal stretch/shrink or reflection.
- No vertical stretch/shrink or reflection.
Therefore, your answers will be:
A = 1, B = 5, C = 1, D = 8
