Interpreting Graphs of Functions
Aligned to F-IF.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
A graph tells a story: intercepts, where it increases or decreases, and maximums or minimums all have real meaning depending on the context.
Worked examples
Example 1
A ball's height vs. time rises to a peak (maximum height) then falls; the x-intercepts are when it leaves and hits the ground.
Example 2
A graph that is flat for an hour means the quantity is unchanging, not that it is zero.
Example 3
Where a graph is steepest is where the quantity changes fastest, which is often the question being asked.
Practice questions
- On a distance-time graph, what does a flat line mean?
- Identify the maximum of a parabola opening downward.
- What do the x-intercepts of a height graph represent?
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
Interpretación de Gráficas de Funciones
Una gráfica cuenta una historia: las intersecciones, los intervalos donde crece o decrece, y los máximos o mínimos tienen un significado real dependiendo del contexto.
Ejemplo 1: La altura de una pelota en función del tiempo sube hasta un punto máximo (altura máxima) y luego baja; las intersecciones con el eje x representan el momento en que la pelota sale y cuando toca el suelo.
Ejemplo 2: Una gráfica plana durante una hora significa que la cantidad no cambia, no que sea cero.
Ejemplo 3: Donde una gráfica es más inclinada es donde la cantidad cambia más rápido, y muchas veces eso es lo que se pregunta.
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