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Question

 

(10.06 HC)
 

f(x)	g(x)
f(x) = 2 tan(3x + π)	g(x) = 3 sin(4x - π) - 2

Using complete sentences, explain how to find the y-intercept for each function and determine which function has the largest y-intercept.

 

Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20 + 30, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

You must show all work.

Answer 1

Calculate the y-intercept:

put x=0:

f(x) = 2 tan(3x + π)

      =2 tan(3(0) + π)

     =2tanπ

    =0

y-intercept of f(x) is 0

g(x)=3 sin(4x - π) - 2

      =3 sin(4(0) - π) - 2

      =3 sin( - π) - 2

     =-3sin( π) - 2

    = -2

y-intercept of g(x) is -2

Therfore, the f(x) has largest y-intercept.

 

Answer 2

H(t) =20cos((pi/15)t)+30

Given equation follows the form: y=Acos(Bx-C)+D, A=amplitude, period=2π/B, C/B=phase shift, D=vertical shift

For given equation: H(t) = 20 cos (pi over 15)t + 30
amplitude=20
B=π/15
period=2π/B=2π/(π/15)=30 sec
Phase shift=0
vertical shift=30

Part 1: How far above the ground is Travis before the ride begins?
H(0) = 20 cos (pi over 15)*0 + 30
H(0) = 20 cos (0) + 30=20+30=50 ft

Part 2: How long does the Ferris wheel take to make one complete revolution?

period=2π/B=2π/(π/15)=30 sec

Part 3: Assuming Travis begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Travis' height above the ground reaches a minimum?
Cos function reaches a minimum at 1/2 period=15 sec
H(15)=20cos(π/15*15)+vertical shift of 30 up
H(15)=20cos(π)+vertical shift of 30
H(15)=20*(-1)+ 30=-20+30=10 ft