OBJ: SWBAT review on converting radicals to exponential form and learn to identify, graph, and model power functions Homework Requests: Questions

Transcription

1 Power Functions 2/4 Obj: SWBAT review converting radicals to exponential form and learn to identify, graph, and model power functions Bell Ringer: x + 2 x 1 = 8 Your turn Turn in on separate sheet of paper: x+ 6 x = -7 Get marker and white board after bell ringer. HW Requests: Questions about Free Fall Project. Homework: pg 190 #1-10

2 OBJ: SWBAT review on converting radicals to exponential form and learn to identify, graph, and model power functions Homework Requests: Questions about Free Fall Project. Homework: pg 190 #1-10

3 Converting Between Radical and Rational Exponent Notation An exponential expression with exponent of the form m/n can be converted to radical notation with index of n, and vice versa, by either of the following formulas: m 1. n n m a a

4 Write in radical form.

5 Write in radical form.

6 Write each expression in radical form. a. Answer: b. Answer:

7 Example 7-2a Write using rational exponents. Answer:

8 Write using rational exponents. Answer:

9 Write each radical using rational exponents. a. Answer: b. Answer:

10 Examples x x.

11 Power Functions 2/7 Mrs. Harton out sick 2/5, 2/6 Obj: SWBAT review converting radicals to exponential form and learn to identify, graph, and model power functions Announcements: Friday Turn in project write ups form everyone and including 1 person from group having scatter plot and chosen equation graphed for picture taking Bell Ringer: 3x x+2 5 x 2 +x 2 = - 2 x 1 Copy notes from overhead Get marker and white board after bell ringer. HW Requests: pg 190 #1-10 (check in) Homework: Complete Power functions WS; pg 190 #55-57

12 Converting Between Radical and Rational Exponent Notation An exponential expression with exponent of the form m/n can be converted to radical notation with index of n, and vice versa, by either of the following formulas: m 1. n n m a a

13 Power Function Definition: y k x where k is a non zero constant called the constant of variation or constant of proportion the constant, p, is the power p Power functions are seen when dealing with areas and volumes Power functions also show up in gravitation (falling bodies) v 4 r 3 3 velocity 16t 2

14 Direct Proportions Direct Variations The variable y is directly proportional to x when: y = k * x k is the constant of variation or constant of proportion Often read as: y varies directly as x Alternatively As x gets larger, y must also get larger k keeps the resulting k the same y x This is a power function

15 Direct Proportions Example: The harder you hit the baseball The farther it travels Distance hit is directly proportional to the force of the hit

16 Direct Proportion Suppose the constant of proportionality is 4 Then y = 4 * x What does the graph of this function look like?

17 Inverse Proportion Inverse Variation The variable y is inversely proportional to x when y Often read as: y varies inversely as x Alternatively y = k * x -1 k x Again, this is a power function As x gets larger, y must get smaller to keep the resulting k the same

18 Inverse Proportion Example: If you bake cookies at a higher temperature, they take less time Time is inversely proportional to temperature

19 Inverse Proportion Consider what the graph looks like Let the constant or proportionality k = 4 Then y 4 x See book for Exit Ticket.

20 Examples: Write the statement as a power function equation. Use k for the constant of variation if one is not given. y = kx varies directly y = k varies inversely x 1. The area A of an equilateral triangle varies directly as the square of the length s of its sides Ans: A = ks 2 2. The current I in an electrical circuit is inversely proportional to the resistance, R, with constant of variation V Ans: I = V/R 3.The energy E produced in a nuclear reaction is proportional to the mass, m, with the constant of variation being c 2 the square of the speed of light. Ans: E= c 2 m 4. The speed p of a free falling object that has been dropped from rest varies as the square root of the distance traveled d with a constant of variation k = 2g Ans: p = 2g d = 2gd