Precalculus

Functions, graphs, logarithms, complex numbers, sequences and matrices.

• Graph a functionType an equation such as y = x² − 4 and draw its graph, then check a point on it.
• Set the graph windowChoose the x and y ranges that the graph screen shows.
• Zoom in and out of a graphUse the zoom tools to magnify a graph or bring back a standard view.
• Trace a graphMove a cursor along a curve to read its x and y values, or jump straight to a chosen x.
• Make a table of valuesList x and f(x) side by side for a function, starting wherever you like.
• Find where two graphs meetFind the point where two curves cross, such as y = x² and y = x + 2.
• Find the zeros (roots) of a graphFind where a curve crosses the x-axis. The example is y = x² − 4, with zeros at x = -2 and x = 2.
• Find a maximum or minimumFind the lowest or highest point of a curve, such as the vertex of y = x² − 2x.
• Work with logarithmsFind log base 10 of a number and undo it with 10 to a power.
• Natural logs and the number eUse ln and eˣ, the natural log and its inverse, based on e ≈ 2.71828.
• Logarithm with any baseFind a log such as log base 2 of 20 by dividing two natural logs.
• Exponential growthFind what a quantity grows to at a fixed percentage rate, and how long it takes to double.
• Complex numbersMultiply complex numbers like (3 + 4i)(1 − 2i) and find a size (modulus) such as |3 + 4i|.
• Enter and multiply matricesStore the matrix [[1, 2], [3, 4]] and multiply it by itself.
• Matrix determinant and inverseFind the determinant and inverse of [[1, 2], [3, 4]].
• Sum a sequence or seriesAdd up the first terms of a sequence, such as 1 + 3 + 5 + … + 19, which comes to 100.
• Graph parametric equationsDraw a curve from x(t) and y(t), such as a circle from cos t and sin t.
• Graph polar equationsDraw curves given as r in terms of θ, such as the three-petal rose r = 2 sin(3θ).