Algebra 1 Common Core Student Edition, Grade 8-9

Pr o b l em 3 Gr ap h i n g a Ho r i zo n t al Tr an sl at i o n

How can you check

t h a t t h e g r a p h is

correct?

You can use th e e qu a tion

to check that points on

the graph are solutions.

What is the graph of y = | x + 5 1?

Got It? 3. W hat is the graph of y = |x - 5|?

y /

Draw t he graph of

y = x + 5| by

translating y = |x|

left 5 units.

sYZZ\*+ 5

1

f = \‘<1

L

.......

*

-1 -< —L I 01 4

The absolute value function is an example of a piecewise function. A piecewise function

is a function th at has different rules for different p arts of its dom ain. For example, w hen

x > 0, |x| = x. W hen x < 0, |x| = —x. A nother exam ple of a piecew ise function is a

step function. A step function is a function th a t pairs every n u m b e r in

an interval w ith a single value. The graph of a step function can look like

th e steps of a staircase.

Each piece of the graph is a horizontal segm ent th a t is m issing its right

endpoint, indicated by an o p en circle.

(^1) L y"]........

• V"X
  S>
  r-y
  ' _
  Gr ap h i n g a St ep Funct i on
  Transportation A school will charter buses so that the student body can attend a
  football game. Each bus holds a maximum of 60 students. Make a graph that models
  the relationship between the number of students x that go to the game by bus and the
  number of buses y that are needed.
  You will need 0 buses for 0 students. As the n u m b er of students increases,
  the n u m b er of buses goes up by 1 every tim e the n u m b er of students
  exceeds a m ultiple of 60. Draw a closed circle w hen the endpoints are part
  of the graph, and th en draw an open point w hen they are not.
  CO^3


• Got It? 4. Make a graph th a t m odels the relationship betw een the
  n u m b e r of students x th at go to th e gam e by bus an d the
  n u m b e r of buses y th at are n e e d e d if each bus holds a
  m axim um of 50 students.
  -QOJ
  E
  y A -
  c
  •S.
  J
  J *1
  )
  X
  0 60 180 300
  Number of Students
  ^ Lesson Check
  Do y o u k n o w H OW?

1. How is the graph of y = |x| - 8 different from the
   graph of y = |x|? How is it th e same?


2. W hat is th e equ atio n for th e translation of y = |x|
   9 units up?


3. W hat is the graph of y = |x + 7|?

3 4 8 Chap t er 5 Linear Funct ions

_. MATHEMATICAL

Do y o u UN DERSTAN D? { g j j PRACTICES

4. Compare and Contrast How are th e graphs of
   y = |x| — 4 a n d y = |x — 4 1 th e sam e? How are they
   different?


5. Error Analysis A s tu d en t is graphing th e equation
   y = |x — 101 a n d translates th e graph of y = |x|
   10 units left. D escribe th e stu d e n t’s error.