Power Functions

1
Power Functions Variations
2
Review of Powers

• Negative Exponents ? Reciprocals Ex. 8-1 1/8
• Rational Exponents ? Radicals Ex. 91/2 3

3
Direct Variations

• As one quantity increases the
  other quantity increases.
• As one quantity decreases the other quantity
  decreases.
• Example Pay varies directly with the number of
  hours worked.
• Example Distance varies directly with the time
  (at a constant rate).

4
Inverse Variations

• As one quantity increases
  the other quantity decreases.
• As one quantity decreases
  the other quantity increases.
• Example Distance a shotput is thrown varies
  inversely with the weight of the shotput.
• Example Boyles Law The pressure of a gas
  varies inversely with the volume (at a constant
  temperature).

5
Direct vs. Inverse Variation

• Y varies DIRECTLY with x to a power.
• Y varies INVERSELY with x to a power.

6
Application Calculation

• The volume of an enclosed gas varies inversely
  with the pressure.
• Write an equation for this statement.
• If the pressure of a 5 L sample of gas is .8 atm,
  what would the volume be at a pressure of 1.4
  atm?
• 
  .

7
Application Calculation

• The power P (in watts) produced by a windmill is
  proportional to the cube of the windspeed (in
  mph).
• Write an equation for this statement.
• If a windspeed of 10 mph generates 15 watts of
  power, how much power is generated by a windspeed
  of 30 mph?
• 
  .

8
Reading Assignment/Notes

• 1) 5 _
• yx, yx2, yx3, y1/x, yvx
• 2) Power 3
• Constant 4/3
• 3) Postive Powers ? Direct
• Negative Powers ? Inverse
• 4) Circumference
• Area of a Circle
• 5) Force of Gravity
• Boyles Law

• 6) Direct
• 7) increasing
• continuous
• 8) both inc dec
• both cont disc
• 9) k is a constant
• n is a positive integer
• 10) Johannes Kepler
• Avg Distance from sun
• Period of Orbit

9
Power Function page 181
10
Which of the following are POWER FUNCTIONS?For
those that are, name the power and constant.

• 1)
• 2)
• 3)
• 4)

11
Monomial Function page 183
12
Which of the following are POLYNOMIALS?For those
that are, name the degree and leading coefficient.

• 5)
• 6)
• 7)

13
Write an equation

• 8) The amount of juice Chaz can drink varies
  directly with the time he drinks.
• 9) The time it takes Mariah to travel 300 miles
  varies inversely with her speed.
• 10) The cost of purchasing 3 CDs varies directly
  with the price of each CD.

14
Tuesday!

• Please trade-n-grade homework. Front ? and
  Back ?
• Page 189 1 34, 51-55, and 58 63.

15
Page 189 1 34

• Power Constant
• 1) 5 -1/2
• 2) 5/3 9
• 3) NOT a power function
• 4) NOT a power function
• 5) 1 c2
• 6) 5 ½ k
• 7) 2 ½ g
• 8) 3
• 9) -2 k
• 10) 1 m

• Leading
• Degree Coefficient
• 11) 0 -4
• 12) NOT a monomial function
• 13) 7 -6
• 14) NOT a monomial function
• 15) 2
• 16) 1 l

16
Page 189 1 34

• 23) The weight, w, of an object
• varies directly with its mass, m.
• constant of variation g
• 24) The circumference, C, of a circle
• varies directly with its diameter, d.
• constant of variation
• 25) The refractive index, n, varies inversely
• with the velocity, v, of the light.
• constant of variation c
• 26) The distance, d, traveled by a free
• falling object dropped from rest
  varies
• directly with the square of its speed
  p.
• constant of variation

• 17)
• 18)
• 19)
• 20)
• 21)
• 22)

17
Page 189 1 34

• 29) g
• 30) a
• 31) d
• 32) g
• 33) h
• 34) d

• 27)
• power -2
• constant 8
• 28)
• power 1/2
• constant -2

18
Page 189 1 34

• Power Constant
• 1) 5 -1/2
• 2) 5/3 9
• 3) NOT a power function
• 4) NOT a power function
• 5) 1 c2
• 6) 5 ½ k
• 7) 2 ½ g
• 8) 3
• 9) -2 k
• 10) 1 m

• Leading
• Degree Coefficient
• 11) 0 -4
• 12) NOT a monomial function
• 13) 7 -6
• 14) NOT a monomial function
• 15) 2
• 16) 1 l

19
Page 189 1 34

• 23) The weight, w, of an object
• varies directly with its mass, m.
• constant of variation g
• 24) The circumference, C, of a circle
• varies directly with its diameter, d.
• constant of variation
• 25) The refractive index, n, varies inversely
• with the velocity, v, of the light.
• constant of variation c
• 26) The distance, d, traveled by a free
• falling object dropped from rest
  varies
• directly with the square of its speed
  p.
• constant of variation

• 17)
• 18)
• 19)
• 20)
• 21)
• 22)

20
Page 189 1 34

• 29) g
• 30) a
• 31) d
• 32) g
• 33) h
• 34) d

• 27)
• power -2
• constant 8
• 28)
• power 1/2
• constant -2

21
P191 51 55, 58 - 63

• 51) 2.21 L
• 52) 3.87 L
• 53) 1.24 x 108 m/sec or
• 124,000,000 m/sec
• 54)
• 54) Double the windspeed
• makes the power 8 X as much.
• 55b) r 231.204 w -0.297

• 58) True
• 60) a
• 62) b
• 63) b