Functions and graphs

  • Cartesian coordinates in two dimensions

  • graph of a set of ordered pairs as a representation of a relationship between two variables

  • linear functions (y = ax + b) and quadratic functions (y = ax2 + bx + c)

  • graphs of linear functions

  • the gradient of a linear graph as the ratio of the vertical change to the

  • horizontal change (positive and negative gradients)

  • graphs of quadratic functions and their properties:

- positive or negative coefficient of x2

- maximum and minimum points

- symmetry

  • sketching the graphs of quadratic functions given in the form:

- y = – (x − p)2 + q

- y = − (x − p)2 + q

- y = – (x − a)(x − b)

- y = − (x − a)(x − b)

  • graphs of power functions of the form y = axn, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these

  • graphs of exponential functions y = kax, where a is a positive integer

  • estimation of the gradient of a curve by drawing a tangent