find all vertical, horizontal, and slant (oblique) asymptotes of rational functions Shows degree comparison for HA, denominator zeros for VA, and polynomial long division for slant asymptotes
Reduce any radical to simplest radical form, add and subtract like radicals, multiply and rationalize, and solve radical equations.prime factorization and perfect square methods
simplify, add, subtract, multiply, and divide rational expressions with full step-by-step LCD calculation, factoring, cross-cancellation, and excluded values shown
Find local maxima, local minima, and absolute extrema of any function using first and second derivative tests. Shows critical points, sign chart, and concavity analysis.
Solve systems of linear equations using Gaussian elimination with partial pivoting. Shows every row operation step, reduced row echelon form, and solution verification.
Calculate absolute value of numbers and expressions. Solves absolute value equations |ax+b|=c and inequalities |x|
Calculate population variance (σ²) and sample variance (s²) from any data set. Shows mean calculation, squared deviations, and standard deviation. Handles raw data and frequency tables.
Find critical values for z-tests, t-tests, chi-square tests, and F-tests at any significance level. Shows rejection regions and p-value interpretation for one-tailed and two-tailed tests.
Convert polar coordinates (r, θ) to rectangular (x, y) and back. Works in degrees and radians. Converts polar equations to rectangular form.
Find all real zeros of any function using bisection method, Newton-Raphson, and rational root theorem. Shows complete step-by-step root-finding process with graph of the function.