The elevation of a landscape is modeled by a cubic function y=f(x)y = f(x)y=f(x), where y y\,y is the height in meters and x x\,x is the horizontal distance from a fixed point. A sketch of the curve y=f(x)y = f(x)y=f(x) shows that it starts from the bottom-left, rises to a local maximum, passes through the yyy-axis at (0,4)(0, 4)(0,4), and then descends to touch the xxx-axis at a local minimum point (3,0)(3, 0)(3,0) before rising again. The curve also intersects the xxx-axis at the point (−5,0)(-5, 0)(−5,0).
On separate diagrams, sketch the curve with equation:
y=f(x−5)y = f(x - 5)y=f(x−5)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
y=f(−12x)\displaystyle y = f\left(-\frac{1}{2}x\right)y=f(−21x)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
Practise Edexcel A Level Maths Functions and Graphs with exam-style questions for A Level Maths. 100 questions covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.