2.6 Transformations of Functions
Ideas in this lesson
- Shift outputs vertically
- Shift inputs horizontally
- Reflect across either axis
- Stretch or shrink vertically
- Stretch or shrink horizontally
- Combine transformations in the stated order
- Recover transformation formulas from actual graphs
- Draw transformed parent functions
- Transform unfamiliar graphs point by point
- Explore step, restricted-domain, and technology graphs
- Classify algebraic functions as even, odd, or neither
- Complete even and odd graphs using symmetry
- Graph absolute values of function outputs
- Interpret transformations in real-world stories
- Prove parity rules and integer-power classification
Shift outputs vertically · Worked example
A point \(P=(0,2)\) lies on y=f(x), whose domain is [−3,5] and range is [−2,7]. For \(g(x)=f(x)+(5)\), locate P’s image and give the new domain and range.
Answer: \((0,7)\); domain [−3,5]; range [3,12].
Only the output changes: (u, w)→(u, w+5).
The mapped point is (0,7).
Inputs remain [−3,5]; add 5 to both range endpoints.
The mapped point is (0,7).
Inputs remain [−3,5]; add 5 to both range endpoints.