O Level MathematicsC2.10 Graphs of functions (construct tables for linear, quadratic, reciprocal).

📈 Mastering Function Graphs: Tables Made Easy!

Edudent Academy
21 Dec 25

Graphs help us **visualise** how numbers behave. Whether it is a straight line in physics, a parabola in economics, or a reciprocal curve in chemistry, being able to construct a table of values and sketch the graph is an essential O-Level skill you’ll use in exams and real-life applications.

Key Ideas for Building Tables

  • Pick sensible x-values (often −2 to 2 or −4 to 4) that show the "shape" of the function.
  • Calculate y-values accurately. **Double-check arithmetic!**
  • Linear:
    y=mx+cy = mx + c
    gives straight lines; only two points technically needed, but use 3–5 for reliability.
  • Quadratic:
    y=ax2+bx+cy = ax^2 + bx + c
    forms a symmetric curve; include the vertex region.
  • Reciprocal:
    y=kxy = \frac{k}{x}
    has two branches and a vertical/horizontal asymptote; avoid
    x=0x = 0
    .

Worked Example: Plotting a Quadratic Curve

Problem: Sketch the graph of
y=x2−2x−3y = x^2 - 2x - 3
for
−1≤x≤5-1 \le x \le 5
using a table of values.

  • Step 1: Choose integer x-values −1, 0, 1, 2, 3, 4, 5.
  • Step 2: Compute y using
    y=x2−2x−3y = x^2 - 2x - 3
    :
    x−1012345y0−3−4−30512\begin{array}{c|ccccccc}x & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & 0 & -3 & -4 & -3 & 0 & 5 & 12\end{array}
  • Step 3: Plot the points and join them smoothly to reveal a U-shaped parabola with vertex near
    (1,−4)(1, -4)
    .

Keep practising by creating tables for different functions—linear, quadratic, and reciprocal—and watch how confidently you draw accurate graphs in the exam!