Algebra 1 Common Core Student Edition, Grade 8-9

Get t i n g Read y!

Graphs can help you

see relationships.

MATHEMATICAL

PRA CTI CES

Volume ■^ ilu ■

Th e graphs below r el at e t h e heig ht o f t h e w at er t o t h e volume

o f t he w at er in each co nt ainer.

Which graph goes wit h which co nt ainer? Ju st i f y your reasoning.

@ Common Core State Standards

^ C D I / N F-IF.B.4... interpret key features o f graphs and tables

W ol MU V-XI U U I lb IU Ixt? lU lG in term s o f the quantities, and sketch graphs showing key

, features... of the relationship...

Two Q uantities mpi.mp 2 .mp 3 .mp 4

A s y o u m a y h a v e n o t ic e d i n th e S o lv e It, th e c h a n g e i n t h e h e ig h t o f t h e w a t e r as th e

volum e increases is related to the shape of the container.

Esse n t i a l U n d e r st a n d i n g Y o u c a n u s e g r a p h s t o v is u a lly r e p r e s e n t th e

r e la t io n s h ip b e tw e e n t w o v a r ia b le q u a n t it ie s as t h e y b o t h c h a n g e.

How can you analyze

the relationship in a

graph?

Read the titles. The

axis titles tell you what

variables are related. The

graph itself represents

the relationship as the

variables change.

Analyzing a Graph

The graph shows the volume of air in a balloon

as you blow it up, until it pops. What are the

variables? Describe how the variables are related

at various points on the graph.

T h e v a r ia b le s a re v o lu m e a n d t im e. T h e v o lu m e

in c re a s e s e a c h t im e y o u b lo w , a n d i t s ta y s c o n s t a n t

e a c h t im e y o u p a u s e t o b r e a th e. W h e n t h e b a llo o n

pops in the m iddle of the fourth blow, the volum e

decreases to 0.

Air in Balloon

234 Chapter 4 An Introduction to Functions