Common Core · High school
HSF-IF.C.7
High school — Graph functions expressed symbolically and show key features of the graph.
High school — Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
The 2 skills that cover it
- Function TransformationsShift, stretch and reflect a parent graph, and read the transformation directly off the equation.Read the lesson →
- Transformations of Any FunctionMove past the parabola: stretch a graph horizontally with f(kx), reflect it in the y-axis, apply several transformations in the right order, track where a single point goes, and do it all to square roots, cube roots, reciprocals, cubics and exponentials.Read the lesson →
What a student should be able to do
- Describe the effect of f(x) + k and f(x + h).
- Describe vertical stretches, compressions and reflections.
- Write the equation of a transformed parent function.
- Sketch a transformed graph from its equation.
- Describe the effect of f(kx) and f(-x), and combine horizontal and vertical transformations in the correct order.
- Find the image of a point on y = f(x) under y = a f(b(x - h)) + k.
- Write the equation of a transformed square root, cube root, reciprocal, cubic, absolute value or exponential parent.
- Classify a function as even, odd or neither, and state the domain and range of a transformed function.