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2 answers:
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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.
Answer:
Option (A)
Step-by-step explanation:
A set of real numbers is a combination of both rational and irrational numbers.
But the elements in the sets of rational and irrational numbers will be different.
In short, rational and irrational number sets are the two subsets of real numbers.
Hence, the number is an element of either the set of rational numbers or the set of irrational numbers.
Option (A) is the correct option.
Answer:
-6 +8d -2c
Step-by-step explanation: