Daily Check

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Daily Check
Solve and graph the following equations.
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Math II
UNIT QUESTION How are absolute value equations
similar to piecewise functions? Standard
MM2A1 Todays Question How do we graph
piecewise functions? Standard MM2A1.a,b
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2.5 Piecewise Functions
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• Up to now, weve been looking at functions
  represented by a single equation.
• In real life, however, functions are represented
  by a combination of equations, each corresponding
  to a part of the domain.
• These are called piecewise functions.

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• One equation gives the value of f(x) when x 1
• And the other when xgt1

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Evaluate f(x) when x0, x2, x4

• First you have to figure out which equation to
  use
• You NEVER use both

X4
X2
X0 This one fits Into the top equation
So 2(4) 1 9 f(4) 9
So 022 f(0)2
This one fits here
So 2(2) 1 5 f(2) 5
This one fits here
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Graph

• For all xs lt 1, use the top graph (to the left
  of 1)
• For all xs 1, use the bottom graph (to the
• right of 1)

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x1 is the breaking point of the graph. To the
left is the top equation. To the right is
the bottom equation.
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Graph
Point of Discontinuity
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Step Functions
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Graph
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Special Step Functions
Two particular kinds of step functions are called
ceiling functions ( f (x) and floor
functions ( f (x) ). In a ceiling function,
all nonintegers are rounded up to the
nearest integer. An example of a ceiling
function is when a phone service company charges
by the number of minutes used and always rounds
up to the nearest integer of minutes.
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Special Step Functions
In a floor function, all nonintegers are rounded
down to the nearest integer. The way we usually
count our age is an example of a floor function
since we round our age down to the nearest year
and do not add a year to our age until we have
passed our birthday. The floor function is the
same thing as the greatest integer function which
can be written as f (x)x.
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Class work
Textbook pg. 51 1-8
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HW Assignment
Textbook p. 52 1-6 and p. 53 26