Graphing Calculator
Plot y = f(x) or equations like x² + y² = 1 with sin, cos, tan, log, sqrt, abs and pow, sliders for a, b, c and a value table. Inequalities are not supported. How it works
Use the Graphing Calculator
Functions
Type the right-hand side of y = f(x), or an equation in x and y such as x^2 + y^2 = 1, which is drawn where both sides are equal. Operators: + - * / ^, brackets, and implicit products such as 2x. A minus sign before a power applies after it: -x^2 is -(x²).
Functions: sin, cos, tan, log (base 10), sqrt, abs, pow(a, b). Constants: pi, e. Sliders: use a, b or c as a number, for example a*x^2 + b, and a slider for it appears. Not available: ln, exp, inequalities, and calculus.
Table of values
| x | y1 | y2 |
|---|---|---|
| -5 | 25 | 0.958924 |
| -4 | 16 | 0.756802 |
| -3 | 9 | -0.14112 |
| -2 | 4 | -0.909297 |
| -1 | 1 | -0.841471 |
| 0 | 0 | 0 |
| 1 | 1 | 0.841471 |
| 2 | 4 | 0.909297 |
| 3 | 9 | 0.14112 |
| 4 | 16 | -0.756802 |
| 5 | 25 | -0.958924 |
About the Graphing Calculator
Type the right-hand side of y = f(x), such as x^2 or sin(x), and the graphing calculator draws the curve on numbered axes that you can pan and zoom; it opens with y1 = x * x and y2 = sin(x). Up to 12 rows share one graph, and a row can also hold an equation in x and y, such as x^2 + y^2 = 1 for a circle. The letters a, b and c get sliders, and a table of values lists each function. It has no ln or exp names.
How formulas are read
| Formula | x | Value |
|---|---|---|
| -x^2 | 3 | -9 |
| -2^2 | 0 | -4 |
| 2^3^2 | 0 | 512 |
| 2^-1 | 0 | 0.5 |
| 2x | 4 | 8 |
| 1/x | 4 | 0.25 |
| sin(pi / 2) | 0 | 1 |
| log(1000) | 0 | 3 |
| sqrt(16) | 0 | 4 |
| abs(-5) | 0 | 5 |
| pow(2, 10) | 0 | 1024 |
| pi | 0 | 3.141592654 |
| e^x | 2 | 7.389056099 |
| log(x) / log(e) | 2 | 0.6931471806 |
Each value is what the formula evaluates to at the x shown, to 10 significant digits. A minus before a power applies after it, and powers group to the right.
Supported inputs
- Operators + - * / ^, brackets, and products without a sign such as 2x
- Functions sin, cos, tan (radians), log (base 10), sqrt, abs and pow(a, b)
- Constants x, pi and e, and the letters a, b and c, each set by a slider from -10 to 10 (1 until moved)
- Equations in x and y with one = sign, such as x^2 + y^2 = 1 or x*y = 1
- Up to 12 saved rows of 300 characters each
Supported outputs
- One curve per row in one of four colors, shown under the row label; rows 5 to 8 and 9 to 12 reuse the same four
- Numbered x and y axes, with grid lines 1, 2 or 5 times a power of ten apart (1 unit at the opening zoom)
- A table of values for each y = f(x) row, to 6 significant digits, from a start x and step you choose (up to 50 rows)
- A message under a row that cannot be read or has no real values in the view
How to use this tool
- Type a formula in a row, for example x^2 - 4, or an equation with one = sign, such as x^2 + y^2 = 1. Press + Add Function for another row.
- Drag the graph to pan. Zoom with the mouse wheel, a two-finger pinch or the zoom buttons, and press Reset view to return to the start.
- Use a, b or c in a formula, such as a*x^2 + b, and move its slider or press Play to watch the curve change.
- Read exact values in the table of values: set the start x, the step and up to 50 rows.
- If a curve is missing, read the message under its row: it names the unsupported function, the unclosed bracket or the unknown name.
Frequently asked questions
- How do I graph a function like y = x^2?
- Type x^2 in a row. The curve is drawn as you type, and + Add Function gives more rows so you can compare, for example x^2 and x^2 - 4 on one graph. To see how a coefficient changes the curve, type a*x^2 + b: a slider appears for a and for b (from -10 to 10, 1 until moved), and with a = 2 and b = -3 the curve passes through 15 at x = 3.
- Can I graph ln(x) or e^x?
- ln and exp are not available, but the constant e is: type e^x for the exponential (7.389056099 at x = 2) and log(x) / log(e) for the natural log (0.6931471806 at x = 2). Plain log is base 10.
- Can I graph a circle or an equation like x^2 + y^2 = 1?
- Yes. Type x^2 + y^2 = 1 in a row and the circle is drawn where both sides are equal. Any equation with one = sign and something on each side works the same way: x*y = 1 gives both branches of a hyperbola, and x = 2 a vertical line. The two rows sqrt(1 - x^2) and -sqrt(1 - x^2) draw the same circle as functions of x.
- Why does -x^2 open downward?
- The minus applies after the power, as in mathematics: -x^2 is -(x^2), which is -9 at x = 3, and -2^2 is -4. Write (-x)^2 when you mean the square of a negative number, which is 9 at x = 3.
- How do I zoom and pan, including on a phone?
- Drag to pan with a mouse, pen or finger. Zoom with the mouse wheel, a two-finger pinch or the zoom buttons, from 10 to 200 pixels per unit. The axes are numbered, and grid lines are 1, 2 or 5 times a power of ten apart: 1 unit at the opening zoom, 5 units zoomed fully out and 0.2 zoomed fully in.
- How do I find where two curves cross?
- Plot both and open the table of values: the curves cross where the two columns match. x^2 and x + 2 cross at x = -1 and x = 2, where both columns read 1 and then 4 in the opening table (x from -5 in steps of 1). There is no intersection finder, so a crossing between table steps needs a smaller step, or set the two formulas equal and solve.
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