Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Square Root Functions: Identifying Domain, Range, and Transformations, Study notes of Abstract Algebra

The objectives, essential question, and key concepts of a lesson on square root functions. Students will learn to identify the domain and range, locate intercepts, determine extremas, and perform transformations of square root functions. The document also includes information on the parent function, intercepts, extrema, and transformations through translations, reflections, and compressions or stretches.

What you will learn

  • What are the extrema of the square root function?
  • How do translations, reflections, and compressions or stretches affect the graph of a square root function?
  • Where are the x and y intercepts of the square root function located?
  • How do transformations affect the domain and range of square root functions?
  • What is the domain and range of the parent square root function?

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

kalia
kalia 🇺🇸

4

(7)

239 documents

1 / 13

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Square Root
Functions
Heather, JoJo, Eden, and Gabe
pf3
pf4
pf5
pf8
pf9
pfa
pfd

Partial preview of the text

Download Square Root Functions: Identifying Domain, Range, and Transformations and more Study notes Abstract Algebra in PDF only on Docsity!

Square Root

Functions

Heather, JoJo, Eden, and Gabe

Objectives

  • Students will be able to identify domain and range of square root functions.
  • Students will be able to locate x and y intercepts of square root functions.
  • Students will be able to determine extremas of square root functions.
  • Students will be able to perform transformations of square roots functions.

Essential Question

  • Which characteristics can be obtained from the graph of a square root function?

Domain and Range of the Parent

Function

Inequality Set Notation:

  • Domain: {x I x ≥ 0}
  • Range: {y I y ≥ 0}

Interval Notation:

  • [0,∞)
  • This applies for both domain and range.

Intercepts

Where the graph crosses the x and y axis.

x-intercept: x=

Y-intercept: y=

Transformations

y= a√x-h + k

a: stretch or compression.

h: strictly for shifting the

graph left or right.

k: strictly for shifting the

graph up and down.

*parent function

Transformations:

Translations

  • The blue dotted line represents the parent function while the red and green solid lines represent translations.
  • The function that represents the solid green line has been shifted to the left 3 and up 2 units.
  • The function that represents the red line has been shifted to the right one unit and down 4 units.

Transformations:

Compressions and Stretches

  • The parent function is represented by the blue dotted line.
  • The function that is represented by the solid red line has been stretched by a factor of 3.
  • The function that is represented by the solid green line has been compressed by a factor of 0.5 or ½.

Worktime

Identify the Domain & Range of these, then state the transformation:

Work Time Answers (ctnd.)

Identify the Domain & Range of these, then state the transformation:

Domain: x ≥ 2 Domain: x ≥ 1 Range: y ≥ −1 Range: y ≤ 4

1 unit right 2 units left 4 units up Reflection across the x-axis Reflection across the x-axis Compression of ¾ Stretch of 2