Graphing Tools

What you can plot

Type a function of $x$ such as $x^2 - 4$, $\sin x$ or $e^{-x}$, an inequality such as $y > 2x + 1$, or a list of points. Up to five rows can be plotted together in different colors, so you can compare a function with its derivative, see where two curves intersect, or check that the points from a table lie on the graph you expect.

Inequalities are shaded on the side that satisfies them. A dashed boundary means the line itself is not included (strict inequality), while a solid boundary means it is. Vertical lines such as $x < 3$ are supported too.

Reading a graph

Zoom and pan to find the features that matter: $x$-intercepts are the real solutions of $f(x) = 0$, the $y$-intercept is $f(0)$, and peaks and valleys mark where the derivative is zero. Gaps and vertical asymptotes show values excluded from the domain. A graph gives approximate values; for exact answers, use the matching algebra or calculus calculator and compare the results.

Seeing transformations

Plotting a function next to a changed version of it is the quickest way to learn transformations. Compare $x^2$ with $(x - 3)^2$ and the parabola moves three units to the right; compare it with $x^2 + 3$ and it moves three units up. Multiplying by a number stretches the curve, and a minus sign in front reflects it across the $x$-axis.

The same idea works for every family of functions. Plot $\sin x$ together with $2\sin x$ and $\sin 2x$ to see the difference between changing the amplitude and changing the period, or compare $e^x$ with $e^{-x}$ to see a reflection across the $y$-axis.

Using the graph with the other calculators

A graph gives approximate answers; the other calculators give exact ones. Graph both sides of an equation to see how many solutions there are and roughly where they lie, then use the equation solver to find their exact values. Plot a function next to its derivative from the derivative calculator to check that the derivative is zero exactly where the graph has a peak or a valley.