Graph Analysis

Graph analysis develops the skill of reading and interpreting the visual behavior of functions. This topic covers finding x- and y-intercepts, analyzing end behavior, identifying vertical and horizontal asymptotes, and applying transformations such as shifts, reflections, and stretches.

Interpreting graphs is essential in data science, economics, and any field that uses charts and plots to communicate trends, thresholds, and predictions.

Practice Tips

• 1To find x-intercepts, set y = 0 and solve; for y-intercepts, substitute x = 0 into the function.
• 2Remember that vertical asymptotes occur where the denominator is zero (and the numerator is not), while horizontal asymptotes depend on the degrees of numerator and denominator.
• 3When applying transformations, work from the inside out: horizontal shifts and stretches first (applied to x), then vertical transformations (applied to the output).