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
- midline y = - 1 ⇒ D = - 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.
Answer:
y = 8x-3
Step-by-step explanation:
A. The extra amount added to the selling price to arrive at the cost price
We're finding the function of (p+3), which means wherever there's an x, we're replacing it with (p+3).
2 (p+3)^2 + 3 (p+3) + 6
Foil out (p+3)^2.
2 (p^2 + 6p + 9) + 3 (p+3) + 6
Distribute.
2p^2 + 12p + 18 + 3p + 9 + 6
Add like terms.
g (p+3) = 2p^2 + 15p + 33
Answer:
$6
Step-by-step explanation:
Hourly rate is $1.5