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Evaluating Piecewise Function

The document provides an overview of piecewise functions including: 1) Defining piecewise functions as functions that use different formulas or functions over different intervals of the domain. 2) Providing an example piecewise function defined as x^2 when x < 2, 6 when x = 2, and 10-x when 2 < x ≤ 6. 3) Explaining that the domain is the set of all x values that can be input to the function, while the range is the set of all y values that are output.

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Shaina Dimla
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961 views32 pages

Evaluating Piecewise Function

The document provides an overview of piecewise functions including: 1) Defining piecewise functions as functions that use different formulas or functions over different intervals of the domain. 2) Providing an example piecewise function defined as x^2 when x < 2, 6 when x = 2, and 10-x when 2 < x ≤ 6. 3) Explaining that the domain is the set of all x values that can be input to the function, while the range is the set of all y values that are output.

Uploaded by

Shaina Dimla
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Piecewise

Function
Mr. Amer Ian D. Gagarin
— Prayer Leader
Objectives

01 Determines 02 Find
the domain and range
piecewise functions;
in piecewise functions;

03 Evaluates 04 Represents
real-life scenario
piecewise functions;
involving piecewise
and
functions.
01
Activity
Evaluating functions.
Plus 1
Mr. Casas St. Lisieux

Mr. Pulido Bl. Gerard

Mr. Lim St. Pio


02
Review
Evaluating functions.
Plus 2
Give me a video solution with full
narration to receive plus 2 in our
first quiz. Items 3 and 5 for boys,
and items 4 and 6 for girls.

Submission is until August 23 if


your schedule is MTh. August 24 if
TF schedule.
Solutions:

Substitute 3 to every x
in the equation
Solutions:

Substitute -5 to every x
in the equation
03
Introduction
What is piecewise looks like?
Piecewise
A piecewise function is a function that is defined by different
formulas or functions for each given interval. It’s also in the
name: piece. The function is defined by pieces of functions
for each part of the domain.
Piecewise
Piecewise
It looks like this:
Example:
● when x is less than 2, it gives x2,

● when x is exactly 2 it gives 6

● when x is more than 2 and less
than or equal to 6 it gives the
line 10-x


(a solid dot means "including",


an open dot means "not including")
Piecewise
And this is how we write it: It looks like this:

(a solid dot means "including",


an open dot means "not including")
Domain???
And this is how we write it: It looks like this:

The Domain (all the values of x that can go into the function)
(using Interval Notation)

(using Set Builder Notation)


Range???
And this is how we write it: It looks like this:

The Range (all the values of y that can go into the function)
(using Interval Notation)

(using Set Builder Notation)


Table of Values/Testing
And this is how we write it: And here are some example values:

X Y

−4 16


 −2 4

0 0

1 1

2 6

3 7
Another

X Y

−1 2

0 2

1 2

2 2

3 3

4 4
Real-life Problem
Doctor’s fee
Doctor’s rate in the Philippines
● Up to 30 minutes costs 500;

● Over 30 and up to 1 hour costs 800; and

● Over 1 hour costs 800 plus 15 per minute

above 1 hour.
Doctor’s rate
● Up to 30 minutes costs 500;

● Over 30 and up to 1 hour costs 800; and

● Over 1 hour costs 800 plus 15 per minute above 1 hour.

{
{
1. You visit for 29 minutes, what is the fee?
2. You visit for 31 minutes, what is the fee?
3. You visit for 1 hour and 58 minutes, what is the fee?
Answers:
{
1. 29 minutes for 500 pesos
2. 31 minutes for 800 pesos
3. 1 hour and 58 minutes for 1,670 pesos
04
More
Examples
05
Cli
ck
me
!

Step Function

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