Graphs of functions and transformations

Learning objectives

Sketch the graph of a function from its equation, from given information or from a real-life context, and transfer a graph accurately from a graphing calculator screen to paper, labelling axes and key points

Use technology to graph functions, including sums and differences of functions, and identify key features: maximum and minimum values, intercepts, symmetry, the vertex, zeros and vertical and horizontal asymptotes

Find points of intersection of two curves or lines using technology, and solve equations graphically or analytically, including equations with no analytic method of solution, in abstract and real-life settings

Apply translations y = f(x) + b and y = f(x − a), reflections in the axes y = −f(x) and y = f(−x), and vertical and horizontal stretches y = p f(x) and y = f(qx), stating the effect of each on points and key features

Combine two or more transformations in the correct order, write the equation of the resulting graph, and describe fully the sequence of transformations that maps one graph onto another

(HL) Sketch the graphs of y = |f(x)|, y = f(|x|), y = 1/f(x), y = f(ax + b) and y = [f(x)]² from the graph of y = f(x), identifying how intercepts, asymptotes and turning points change