The viewing window is your frame: The GDC graph is only as good as the window you choose.
A bad window hides the key features — intercepts, turning points, asymptotes — that IB questions ask about.
Getting the window right is a skill, not an afterthought.
The four settings you control are Xmin, Xmax, Ymin and Ymax.
Together they define the rectangle of the coordinate plane that appears on screen.
| Setting | What it controls | Typical starting value |
|---|---|---|
| Xmin | Left edge of the x-axis | −10 (or 0 for time/distance) |
| Xmax | Right edge of the x-axis | 10 (adjust for context) |
| Ymin | Bottom edge of the y-axis | −10 (or 0 for positive quantities) |
| Ymax | Top edge of the y-axis | 10 (or higher for cost/population) |
| Xscl / Yscl | Tick-mark spacing | 1 or 2 (cosmetic only) |
Start with ZoomStd or ZoomFit, then adjust: On a TI-84: press ZOOM → 6 (ZStandard) for a −10 to 10 window, or ZOOM → 0 (ZoomFit) to auto-scale.
On a Casio fx-CG50: press SHIFT+F3 (V-Window) and type values manually.
Then zoom in on the interesting part.
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
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x-intercept = zero; intersection = two curves meeting: The x-intercept of f(x) is where f(x) = 0 — the curve crosses the x-axis.
An intersection point is where two different functions are equal: f(x) = g(x).
The cost of hiring a bicycle is C(d) = 60d + 10 for d ≥ 3.
A competitor charges G(d) = 50d + 40.
Find the number of days for which both companies charge the same amount.
Step by step
- Enter both functions in Y1 and Y2 on the GDC.
- Choose Xmin = 0 and Xmax = 10 (a sensible range for days). To find Ymax, test the cost at the right edge: C(10) = 60(10) + 10 = 610 and G(10) = 50(10) + 40 = 540. The larger value is 610, so Ymax = 700 gives the line some breathing room at the top. Ymin = 0 (cost cannot be negative).
- Use Calc → Intersect (TI: 2nd TRACE 5; Casio: G-Solv → ISCT).
- Read the intersection coordinates.
Final answer
After 3 days both companies charge $190.
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Always check the domain: The GDC finds all mathematical intersections.
But if the model only applies for d ≥ 3 (as above), reject any intersection at d < 3.
The GDC does not know about domain restrictions — you do.
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Local max/min = the peak or trough on the visible curve: The GDC can locate turning points numerically.
You do not need calculus — just the right menu.
On TI: 2nd TRACE → Maximum or Minimum.
On Casio: G-Solv → MAX or MIN.
A dolphin's height (metres) during a jump is h(d) = −0.5d² + 3d, where d is horizontal distance.
Find the maximum height and the horizontal distance at which it occurs.
Step by step
- Enter h(d) = −0.5x² + 3x in Y1.
- Choose a window: Xmin = 0, Xmax = 7, Ymin = −1, Ymax = 6.
- Use Calc → Maximum. Move left bound to x = 0, right bound to x = 6, guess near the peak.
- GDC returns the maximum point.
Final answer
Maximum height = 4.5 m at horizontal distance d = 3 m.
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
State coordinates, not just the y-value: IB mark schemes usually want both the x-coordinate (where the max occurs) and the y-coordinate (the maximum value).
Write: "Maximum at (3, 4.5)" — not just "4.5 metres".
The GDC gives numbers — you give meaning: Every coordinate the GDC returns must be interpreted in the context of the problem.
"x = 3" means nothing on its own; "after 3 days" or "at distance 3 metres" is the answer.
✗ Incomplete answer
- x = 3, y = 190
- Maximum = 4.5
- Intersection at x = 6
✓ Full IB answer
- After 3 days, both companies charge $190.
- The maximum height of the dolphin is 4.5 m, occurring at a horizontal distance of 3 m.
- The two functions are equal when x = 6 hours; revenue = $540.
Round appropriately: IB questions say "give your answer correct to ... decimal places" or "to the nearest integer".
If no rounding instruction is given, 3 significant figures is standard.
Never give a 10-digit GDC readout as your answer.
GDC output checklist
- Did you set a window that captures ALL key features?
- Did you use the correct menu (zero / intersect / max / min)?
- Did you interpret the coordinate using the units from the question?
- Did you check whether the answer is within the domain?
- Did you round to the precision asked for?
IB-style question — interpret GDC output in context [4 marks]
A theme-park ride's profit, P thousand dollars, after operating for t hours is modelled by P(t) = −0.5t² + 6t − 4. A student enters the model into a GDC and reports that the curve has a maximum point at (6, 14) and an x-intercept at (0.7, 0).
(a) State what the maximum point tells you about the ride's profit.
(b) State what the x-intercept at t ≈ 0.7 tells you about the ride.
Step by step
- (a) Read the maximum point as a coordinate: the t-value is when, the P-value is how much. The maximum is at t = 6, P = 14.
- So the ride makes its greatest profit, $14 000, after 6 hours of operation.
- (b) The x-intercept is where P = 0 — the break-even point, where profit changes from negative to positive.
- So after about 0.7 hours (around 42 minutes) the ride first breaks even; before that it is running at a loss.
Final answer
(a) The greatest profit is $14 000, reached after 6 hours. (b) The ride first breaks even after about 0.7 hours; before that it makes a loss.