Use a graphic display calculator to explore graphs
Enter functions, build value tables, plot points and use a GDC to locate zeros, extrema, vertices and intersections.
Section 3 · Functions
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you inspect if the graph looks blank after entering a function?
What you will learn
- Sketch graphs and produce tables of values on a GDC
- Plot points and estimate zeros, local extrema and intersections
- Use the same workflow on unfamiliar functions
Set the viewing window and inspect the graph
Enter the function with brackets around grouped expressions and choose a window that includes the feature asked for. Check the horizontal and vertical scales before reading a value.
A table of values supports a sketch and helps locate a root or turning point. If a feature lies outside the window, adjust the scale rather than assuming it does not exist.
Use calculator features as evidence to interpret
A zero is an x-value where y = 0; a local maximum or minimum is a turning feature near the selected interval. An intersection is shared by two graphs, so both coordinates should satisfy both equations.
For unfamiliar functions, graph and table are tools, not explanations. Record the interval, units and sensible rounding, then check an approximate result by substitution when possible.
Pause and explain
At an intersection of y = f(x) and y = g(x), what is true?
Worked example
Use a graph or table to estimate where y = x² − 5x + 4 crosses the x-axis.
Show the worked solution
- Enter y = x² − 5x + 4 and choose a window containing x values 0 to 5.
- The graph crosses near x = 1 and x = 4; a table around each crossing narrows the estimates.
- Check: (1)² − 5(1) + 4 = 0 and (4)² − 5(4) + 4 = 0.
Answer Zeros x = 1 and x = 4.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A GDC table for f(x) = x² − 4 shows f(1) = −3 and f(2) = 0. Describe the x-intercept at x = 2 and explain a graph check.
Give me a hint
A zero occurs where the output is zero; check the value in the entered function.
Compare my reasoning
- f(2) = 2² − 4 = 0.
- The graph therefore crosses or touches the x-axis at (2, 0).
- A graph window around x = 2 should show the point on the axis.
The x-intercept is (2, 0), confirmed by f(2) = 0.
Look for these in your work
- Output interpreted as a zero
- Ordered pair given
- Calculator result checked algebraically
Two plotted lines intersect at approximately (3, 7). What should you do to validate that estimate if their equations are available?
Give me a hint
Substitute x = 3 into both rules and compare the predicted y-values with 7.
Compare my reasoning
- Evaluate each function at x = 3.
- Both outputs should be close to 7.
- If they differ materially, refine the graph window or intersection estimate.
Check f(3) and g(3); both should be approximately 7.
Look for these in your work
- Both rules checked
- Coordinates interpreted consistently
- Approximation refined when needed
A GDC finds a local maximum in a model of daily visitors. State what you would record so another learner can assess the result and why the maximum may not describe the whole data set.
Give me a hint
Include the point, window and units; distinguish a local feature from the global range of observed values.
Compare my reasoning
- Record the estimated coordinates and units of the maximum.
- State the graphing window and any rounding.
- A local maximum is only highest nearby; a different interval or endpoint may have a larger value.
Record point, units, window and rounding; distinguish local from global maximum.
Look for these in your work
- Feature specified
- Window and units included
- Local/global distinction made
Common mistakes
- Using a window that hides a root
- Confusing a y-value with the corresponding x-value
- Reading an intersection from only one graph
- Reporting calculator digits without context or checking
What can you explain now?
What does a zero of f mean on the graph y = f(x)?
Compare with the explanation
An x-value where f(x) = 0
At a zero the graph meets the x-axis.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How can a table, graph window and substitution check work together to support a GDC result?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.