Relations, Functions and Graphs
Relations, functions and graphs
Candidates must read and plot coordinates, understand relations as sets of ordered pairs, and use function notation. Know domain and range, identify whether a relation is a function, and interpret mappings. For graphs, find gradients and intercepts, draw straight lines from equations, solve simultaneous equations graphically, and sketch quadratic curves using roots, turning point and intercept. Distance-time and conversion graphs may also appear.
Common traps include reversing the gradient formula, ignoring the sign of the gradient, and reading values from a graph without using the stated scale. A vertical line test distinguishes a function from a relation: if a vertical line crosses a graph more than once, the relation is not a function. Do not confuse the x-intercept with the y-intercept. When solving graphically, the solution is the point of intersection, so give both coordinates. For a line y = mx + c, m is the gradient and c is the y-intercept.
Worked example: find the equation of the line through (2, 5) and (6, 13). Gradient = (13 - 5) / (6 - 2) = 8 / 4 = 2. Using y = mx + c: 5 = 2(2) + c, so c = 1. The equation is y = 2x + 1. Check with the second point: 2(6) + 1 = 13.
Rule of thumb: always label the axes and check the gradient by moving one unit horizontally and reading the vertical change.