Scribd
Upload
77 views1 page

Variables and Functions Guide

The document defines key variable terms: independent variables control dependent variables and are represented by x, while dependent variables depend on independent variables and are represented by y. It provides examples of identifying independent and dependent variables in situations. The document also defines domain as the set of acceptable inputs for a function and range as the set of resulting outputs. It gives examples of finding the domain and range from mappings, ordered pairs, and equations, noting restrictions like denominators cannot be zero.

Uploaded by

69 taguro Yujin
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
77 views1 page

Variables and Functions Guide

The document defines key variable terms: independent variables control dependent variables and are represented by x, while dependent variables depend on independent variables and are represented by y. It provides examples of identifying independent and dependent variables in situations. The document also defines domain as the set of acceptable inputs for a function and range as the set of resulting outputs. It gives examples of finding the domain and range from mappings, ordered pairs, and equations, noting restrictions like denominators cannot be zero.

Uploaded by

69 taguro Yujin
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
You are on page 1/ 1

VARIABLES

Variable – any characteristic, number, or quantity that can be measured or counted.


1.) Independent variable is a variable that will change by taking on different values. In a relation, independent
variable controls the dependent variable. It is represented by the 𝑥 -variable or abscissa.
2.) Dependent variable is a variable that is affected by the independent variable. In a relation, dependent
variable depends on the independent variable. It is represented by the 𝑦 -variable or ordinate.

Practice: Given each situation below, determine if each variable controls or depends on the other by
supplying the missing terms. independent – controls dependent – depends
on
1. Doris was looking for a job. She noticed that the higher paying job requires higher education. Higher
education is the independent variable because it controls the variable “higher paying job”.

2. Roberto regularly buys dressed chicken at the market. The cost of the chicken is the dependent variable
because it depends on the number of kilograms of chicken.

3. Paul planned to tile his floor. He measures the length and the width of his floor to calculate the area. The
area of the floor is the _____________ variable because it _____________ the length and the width of the floor.

4. Jana auditioned in the “Pinoy Got Talent” competition. Her performance got a vote of 4 “Yes” from the
judges. Jana’s performance is the ________________ variable because it ________________ the judges’ vote.

5. Erick’s math grade in the first quarter was 98%. He had completed all 10 requirements. The number of
requirements completed is the ________________ variable because it ________________ the math grade.

DOMAIN and RANGE of a Function


DOMAIN of a function is the set of all acceptable inputs. Generally, domain is the set of 𝑥 –values (abscissa)
for which the function is defined.

RANGE of a function is the set of resulting outputs. Generally, range is the set of 𝑦 –values (ordinate) of a
function.

Finding the Domain and Range


I. MAPPING/DIAGRAM
Determine the domain and range described
by the mapping on the right:

Domain: _________________________ Range: _________________________

II. ORDERED PAIRS


Determine the domain and range of the function: {(0, −3), (2,5), (−1, −1), (−3,15), (1, −1)}
Domain: _________________________ Range: _________________________

III. EQUATION
RESTRICTIONS for Domain and Range:
A.) For fractions: The denominator must be not equal to zero since division by zero is undefined.
B.) For radicals with even indices: The radicand must be nonnegative.

Examples:
1.) Find the domain and range of the function 𝑦 = 𝑥2 − 9
3
2.) Find the domain and range of the function 𝑓(𝑥) = 𝑥
Recall the restriction: Denominator cannot be zero.
2𝑥 + 1
3.) Find the domain and range of the function 𝑓(𝑥) = 𝑥+2
Recall the restriction: Denominator cannot be zero.
4.) Find the domain and range of the function 𝑓(𝑥) = √ 𝑥 − 4 .
Recall the restriction: For radicals with even indices, the radicand must be nonnegative.

You might also like