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6.3 – Square Root Functions and Inequalities Day 1.

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Presentation on theme: "6.3 – Square Root Functions and Inequalities Day 1."— Presentation transcript:

1 6.3 – Square Root Functions and Inequalities Day 1

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

3

4 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!

5 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!

6 Example 1: Identify the domain and range of

7 Example 2: Identify the domain and range of

8

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

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

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

12 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}

13 6.3 – Square Root Functions and Inequalities Day 2

14 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.

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

16 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?

17 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.

18 Example 2: Graph

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

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

21 6.3 – Cube Root Functions Day 3

22 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

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

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

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

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

27 Example 4:

28 Example 5: (You try)

29 Ticket Out:


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