18 graphing calculator tricks that save time

Graphing

1. Restrict a graph to an interval

Add a condition in braces after any expression to draw only part of it: y = x^2 {0 < x < 2}. It works for inequalities and parametric curves too, and is the quickest way to draw a piecewise sketch.

2. Let sliders find the right shape

Type a formula with letters you haven’t defined, like y = a sin(b x), and accept the sliders. Dragging a and b is the fastest way to understand what each parameter does, and pressing play animates them.

3. Draw a family of curves in one row

A list inside an expression draws one curve per element: y = [1, 2, 3] x draws three lines. Use it to compare members of a family without typing each one.

4. Type equations as they are

There is no need to solve for y. x^2 + y^2 = 9 draws a circle, and any equation in x and y is drawn as an implicit curve.

5. Shade inequalities, and systems of them

y > x^2 - 2 shades the region above the parabola. Add more inequalities and the overlap is the solution of the system. Strict inequalities get dashed boundaries automatically.

6. Polar and parametric curves need no mode switch

Start a row with r = for a polar curve, such as r = 1 + cos(theta), or write a pair in t for a parametric curve: (cos(t), sin(2t)).

Calculus

7. Graph a derivative without working it out

Define a function, f(x) = x^3 - 3x, then graph y = f'(x). The derivative is computed symbolically and updates as you change f. The Analysis tab shows its formula.

8. Click a curve to find roots, extrema and intersections

Select any curve and its roots, maxima, minima, intercepts and intersections with every other curve are marked and listed, refined to about twelve digits. This replaces the zero, maximum and intersect menus on a handheld.

9. Integrals come with an error estimate

int(e^(-x^2), x, -Infinity, Infinity) evaluates to 1.77245385091 (that is √π) and reports how accurate the result is. Infinite bounds are fine.

10. Sums too

sum(1/n^2, n, 1, 1000) adds the terms with compensated (Kahan) summation, so rounding errors don’t pile up over long sums.

11. Ask the algebra panel

The Algebra tab factors, expands, simplifies and solves, finds antiderivatives, limits and Taylor series, and shows the steps of a derivative. Its results are expressions you can graph with one click.

Data

12. Fit any model with ~

With data in a table, y1 ~ m x1 + b fits a line. Any formula works: y1 ~ a e^(b x1), y1 ~ a sin(b x1 + c). Turn on the 95% band and the residuals to judge the fit, not just R².

13. Statistics on lists

Name a list, D = [3, 1, 4, 1, 5, 9, 2, 6], then mean(D), median(D), stdev(D) or boxplot(D, 1, 0.5). Paste a column from a spreadsheet into a table for bigger data sets.

Beyond the usual

14. Calculate with units

9.81 m/s^2 * 3 s gives 29.43 m/s. Add to km/h to convert. Adding incompatible units is an error, not a silent mistake.

15. Slope fields in one line

dy/dx = x - y draws the slope field; click the graph to add solutions through any point.

16. 3D is the same language

Switch to 3D and type z = sin(x) cos(y), or any equation in x, y and z. Export STL to 3D-print it.

17. Make it interactive with actions

With a = 0 defined, an action like a -> a + 1 becomes a button that adds 1 to a each time it is clicked. Combine actions with a ticker to build simulations and simple games.

18. Share the exact graph with a link

Share puts the entire graph inside the link, so the person who opens it sees exactly what you see. Nothing is uploaded. Use version history to go back to any earlier state.