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**6.3 – Square Root Functions and Inequalities**

Day 1

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

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**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!

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**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!

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Example 1: Identify the domain and range of

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Example 2: Identify the domain and range of

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

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

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

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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}

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**6.3 – Square Root Functions and Inequalities**

Day 2

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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

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

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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?

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**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.

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Example 2: Graph

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

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

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6.3 – Cube Root Functions Day 3

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**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

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**Range of Cube Root Functions:**

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

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

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

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

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

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

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

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