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.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.