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

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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