# 6.3 – Square Root Functions and Inequalities

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6.3 – Square Root Functions and Inequalities
Day 1

Vocabulary: Square Root Function – a function that contains the square root of a variable. - A type of radical function.

Domain of Square Root Functions:
Domain: (What type of #’s can/cannot be underneath a square root???) • # CANNOT be negative, so… the # (or expression) has to be > 0!

Range of Square Root Functions:
Range: (What type of #’s will result from square rooting a #???) • Answers WILL NOT be negative, so… the y-values resulting from the square root function have to be > 0!

Example 1: Identify the domain and range of

Example 2: Identify the domain and range of

Example 3: Graph the function. State the domain and range.

Example 4: Graph the function. State the domain and range.

Example 5: Graph the function. A. B. C. D.

Ticket Out: State the domain and range of the function. Hw – pg. 403, #13 – 16, 22 – 28 even A. D: {x | x ≥ –1}; R: {y | y ≤ –4} B. D: {x | x ≥ 1}; R: {y | y ≥ –4} C. D: {x | x ≥ –1}; R: {y | y ≤ 4} D. D: {x | x ≥ 1}; R: {y | y ≤ 4}

6.3 – Square Root Functions and Inequalities
Day 2

Example 1: When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function

Example 1: a. Graph the function in the domain {a|a ≥ 0}.

Example 1: b. What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?

Square Root Inequalities
An inequality involving square roots. Graph using same method as other inequalities. - Solid or dashed line??? - Shade above or below??? (Test point.) * From endpoint, shade straight up/down.

Example 2: Graph

Example 3: Graph A. B. C. D.

Ticket Out: Graph Hw – pg. 403, #8, 29, 30, 32 – 38 even

6.3 – Cube Root Functions Day 3

Domain of Cube Root Functions:
Domain: (What type of #’s can/cannot be underneath a cube root???) • Any # can be put under a cube root! Domain: All real numbers

Range of Cube Root Functions:
Range: (What type of #’s will result from cube rooting a #???) • Answers could be ANY #! Range: all real numbers

Example 1: Graph the function. State the domain and range. (Parent function for cubed roots.)

Example 2: Graph the function. State the domain and range.

Example 3: (You try) Graph the function. State the domain and range.

Example 4: Graph the function. 𝑓 𝑥 ≤ 𝑥−1

Example 5: (You try) Graph the function. 𝑓 𝑥 >−2 3 𝑥−3 −1

Ticket Out: Graph the function. 𝑓 𝑥 >− 3 𝑥 +3 Hw – Worksheets