4.Graph a sine function whose amplitude is 5, period is6, midline isy=2, andy-intercept is(0,2). The graph isnota reflection of the parent function over thex-axis.

The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

5.

The graph off(x)=cos(x)is transformed to a new function,g(x), by stretching it horizontallyby a factor of 4 and shifting it1 unit up.

What is the equation of the new functiong(x)?

g(x)=

6.

Enter the amplitude of the functionf(x).

f(x)=34cos(3x)+4

7.

What is the equation of the midline for the functionf(x)?

f(x)=3cos(x)2.5

8.

What is the frequency of the functionf(x)?

f(x)=14cos(2x)+5

Express the answer in fraction form.

9.

Graph the function.

f(x)=2sin(x)

Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

10.

Graph the function.

f(x)=sin(x2)

Use the sine tool to graph the function. The 1st point must be on the mid-line and the 2nd point must be a maximum or minimum value on the graph closest to the first point.

11.

In the functionf(x),xis replaced with 2xand 1 is added to the function.

f(x)=3sinx

What effect does this have on the graph of the function?

• The graph is vertically stretched by a factor of 2 and shifts down 1 unit.
• The graph is horizontally compressed by a factor of 2 and shifts up 1 unit.
• The graph is vertically stretched by a factor of 2 and shifts up 1 unit.
• Thegraphishorizontallycompressedbyafactorof2andshiftsdown1unit.
• 9.

Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70F in the morning, rises to a high of 80F, falls to a low of 60F, and then rises to 70F by the next morning.

What is the equation for the sine functionf(x), wherexrepresents time in hours since the beginning of the 24-hour period, that models the situation?

Enter your answer in the box.

f(x)=

10.

The table of values shows the height of a car of a Ferris wheel as it travels in a circular motion.

Which statements are true?

Selecteachcorrect answer.

• The radius of the Ferris wheel is 26 m.
• If the car is loaded at 0 s, then people are loaded at the lowest height of the Ferris wheel.
• The car makes a complete revolution in 8 s.
• The maximum height of the Ferris wheel above ground is 40 m.

0	6
2	26
4	46
6	26
8	6
10	26
12	46
14	26
16	6

11.

Graph the function

f(x)=sin (x)-2

Answer:

12.

Graph the function

f(x)=cos(2x)+1

answer:

13.

A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulums furthest distance to either side was 6 in. Graph the function that represents the pendulums displacement as a function of time.

Write an equation to represent the displacement of the pendulum as a function of time.

Graph the function.

Answer: