It is given that f(x)=x(x−b)(x+4)f(x) = x(x - b)(x + 4)f(x)=x(x−b)(x+4) where 0<b<40 < b < 40<b<4.
Sketch the curve with equation y=f(x)y = f(x)y=f(x), showing on your sketch the coordinates, in terms of b b\,b where appropriate, of the points where the curve meets the xxx-axis.
Sketch the curve with equation y=f(3x)y = f(3x)y=f(3x).
State, in terms of b b\,b where appropriate, the coordinates of the points where the curve y=f(3x)y = f(3x)y=f(3x) meets the xxx-axis.
33 exam-style questions on OCR (MEI) A Level Maths 1.4 Graphs, covering 1.4.1 Graphs of functions, 1.4.2 Intersection points with axes, 1.4.3 Completing the square for a quadratic curve, 1.4.4 Sketch graphs of simple functions, 1.4.5 Stationary points when curve sketching, 1.4.6 Graphs of reciprocal-type functions, 1.4.7 Single transformations of graphs, 1.4.8 Combined transformations of graphs (A-level only), and 1.4.9 Stationary points of inflection (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.