Type a function of x and see it drawn. Standard shapes such as x², x³, 1/x and y = 2x are one click away, and the axis ranges are yours to set.
| Function | Shape | What to notice |
|---|---|---|
| y = x | Straight line through the origin | Gradient 1, odd symmetry |
| y = 2x | Straight line, steeper | Gradient 2, still through the origin |
| y = x² | Parabola opening upward | Minimum at the origin, symmetric about the y axis |
| y = x³ | Rising S-curve | Point of inflection at the origin, odd symmetry |
| y = 1/x | Rectangular hyperbola, two branches | Asymptotes along both axes; undefined at x = 0 |
| y = 1/x² | Both branches above the axis | Always positive, asymptotic to both axes |
| y = x + 1/x | Two branches with a gap | Minimum 2 at x = 1, maximum −2 at x = −1 |
Three things carry most of the marks. Intercepts: set x = 0 for the y intercept, solve f(x) = 0 for the x intercepts. Asymptotes: a vertical asymptote sits wherever the denominator vanishes, and a horizontal one is the value the curve approaches as x runs off to ±∞. Symmetry: if f(−x) = f(x) the curve is symmetric about the y axis (even, like x²); if f(−x) = −f(x) it has rotational symmetry about the origin (odd, like x³ and 1/x).
At x = 0 the function is undefined, and either side of it the values run to opposite infinities. Joining the two branches with a line through the origin, which many plotters do by accident, draws something that is not the graph at all. The plotter above breaks the curve whenever consecutive samples jump further than the visible height, so asymptotes appear as gaps rather than as near-vertical strokes.
The odd result that the local minimum (2) sits above the local maximum (−2) is correct here, and is a standard trap — the two turning points are on different branches, so they never have to be ordered.
Type x^2 into the function box. It draws a parabola with its minimum at the origin, symmetric about the y axis, rising equally on both sides.
It is a rectangular hyperbola with two separate branches, one in the first quadrant and one in the third. Both axes are asymptotes and the function is undefined at x equals zero.
Two branches with a vertical asymptote at x equals zero. It has a local minimum of 2 at x equals 1 and a local maximum of minus 2 at x equals minus 1, and it approaches the line y equals x for large values of x.
x squared is a parabola that stays above the axis and is symmetric about the y axis. x cubed is an S-shaped curve that takes negative values for negative x and has rotational symmetry about the origin.
Polynomials, roots, reciprocals, exponentials, logarithms and all the trigonometric and inverse trigonometric functions. Use the caret for powers, sqrt for square root, ln for natural log and log for base ten.