Lizzie has 12 pounds of clay and wants to use all of it. She does not need to make all of the projects, and may make more than o
ne of any project. Describe a plan for Lizzie to use 12 pounds of clay making projects from the chart. Show how you know she will use exactly 12 pounds of clay with this plan, with no clay left over. 
1 answer:
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Answer:
- See the graphs attached and the explanation below
Explanation:
The most simple sine function, considered the parent function, is:
That function has:
- Midline, also known as rest or equilibrium position: y = 0
- Minimum: - 1
- Maximum: 1
- Amplitude: the distance between a minimum or a maximum and the midline = 1
- period: the interval of repetition of the function = 2π
The more general sine function is:
That function has:
- Midline: y = D (it is a vertical shift from the parent function)
- Minimum: - A + D
- Maximum: A + D
- Amplitude: A
- period: 2π/B
- phase shift: C (it is a horizontal shift of the from the parent function)
Now, you have to draw the sine function with the given key features:
- Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
- Amplitude, A = 3
- midline y = - 1 ⇒ D = - 1
- y-intercept = (0, -1)
Substitute the know values and use the y-intercept to find C:
Substitute (0, -1)
Hence, the function to graph is:
To draw that function use this:
- Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
- Minima: 3(-1) - 1 = - 3 - 1 = -4
- y-intercept: (0, - 1)
- x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
- first point of the midline: (0, -1) it is the same y-intercept
With that you can understand the graphs attached.
