Common Core · High school
HSF-BF.B.3
High school — Identify the effect on a graph of replacing f(x) by f(x) + k, k·f(x), f(kx) and f(x + k).
High school — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx) and f(x + k) for specific values of k; find the value of k given the graphs; recognise even and odd functions from their graphs and algebraic expressions.
The 3 skills that cover it
- Function TransformationsShift, stretch and reflect a parent graph, and read the transformation directly off the equation.Read the lesson →
- Graphs of Sine & CosineUnroll the unit circle into a wave: read the amplitude, period, midline and phase shift of y = a sin(b(x - h)) + k off its equation and its graph, and write the equation of a wave you are shown.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.
- State the amplitude, period and midline of a sine or cosine function from its equation.
- Find the phase shift and the direction of a reflection.
- Write the equation of a sine or cosine wave from its features or its graph.
- Model a periodic situation, such as a tide or a wheel, with a sinusoidal function.
- 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.