Graphing Key Features of Functions
Aligned to F-IF.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
To graph a function, identify its key features: intercepts, asymptotes, increasing or decreasing behavior, and any end behavior. Exponential graphs have a horizontal asymptote; polynomials have zeros; logs have a vertical asymptote.
Worked example
Graph f(x) = 2^x. The y-intercept is (0, 1) since 2^0 = 1. It passes through (1, 2) and (2, 4), and as x decreases it approaches the horizontal asymptote y = 0 without touching it. The function is always increasing.
Practice questions
- State the y-intercept and asymptote of f(x) = 3^x.
- Find the zeros of f(x) = x^2 − 9 and sketch its shape.
- Describe the vertical asymptote of f(x) = log(x).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Graficar Características Clave de Funciones
Para graficar una función, identifica sus características clave: intersecciones, asíntotas, comportamiento creciente o decreciente, y el comportamiento en los extremos. Las gráficas exponenciales tienen una asíntota horizontal; los polinomios tienen ceros; los logaritmos tienen una asíntota vertical.
Ejemplo: Grafica f(x) = 2^x. La intersección con el eje y es (0, 1) porque 2^0 = 1. Pasa por (1, 2) y (2, 4), y cuando x disminuye se acerca a la asíntota horizontal y = 0 sin tocarla. La función siempre es creciente.
More Functions lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required