Convert y = 8x^2-80x-32 to vertex form by completing the square.
2 answers:
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Answer:
a) 2π; [-3,5]; b) 2π; [-2,2]
Step-by-step explanation:
(a) y = 1 + 4sin x
The general form of a sine function is
y = A(sin(B(x - h)) + k
where
|A| = amplitude
2π/B = T =period
h = phase shift (horizontal shift, to the right if x > 0)
k = vertical shift (midline is y = k)
Your function is
y = 1 + 4sin(x)
Comparing terms, we find that
h = 0
k = 1
A = 4
B = 1
The amplitude is 4.
The midline is y = 1.
The horizontal shift is 0.
(i) Period
T = 2π/B = 2π/1 = 2π
(ii) Graph
The graph of the function is the first figure below.
(iii) Image set
The image of a function is the set of all possible values it can have.
If f(x)= 1 + 4sin(x), the domain of the function is (-∞,∞).
The corresponding values of y can take any value from -3 to 5.
The image set is [-3,5].
(b) y = 2sin(x - 3)
h = 3; k = 0; A = 2; B = 1
The amplitude is 2
The midline is y = 0.
The horizontal shift is 3 radians to the right.
(i) Period
T = 2π/B = 2π/1 = 2π
(ii) Graph
The graph of the function is the second figure below.
(iii)Image set
If f(x) = 2sin(x - 3), the domain of the function is (-∞,∞)
The corresponding values of y can take any value from -2 to 2.
The image set is [-2,2].
Answer:
Step-by-step explanation:
Here we have a number in the ones place, 2, and a number in the tenths place, 4.
- Any number in front of the decimal becomes the whole number in front of the mixed number fraction
- The numerator will be any number after the decimal
- The denominator will be the value of the place the number after the decimal is in
Here our whole number is 2, the numerator is 4, and it is in the tenths place, so our denominator will be 10
Our fraction becomes which then turns into the improper fraction
and then simplifying if needed becomes
after dividing the fraction by 2