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 AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
