y = -2sin(x) - 4
Amplitude =_________
Period = __________
Two x- intercepts = __________
y - intercept = _____________
Domain = ___________
Range = ____________
Shift along x = ____________
Shift along y = _____________
Kind of reflection = ______________
y = -2sin(x) - 4
Amplitude = 2_________
Period = 2 pi__________
Two x- intercepts ----It never hits y = 0
y - intercept = -4 _____________
Domain = all real x___________
Range = -2 </= y </= -6
Shift along x = none____________
Shift along y = -4_____________
Kind of reflection = it is an odd function
Can you do one more please? This one is the same as seven of my other practice problems
y = sin(-3x + 3)
Amplitude =
Period =
Two x- intercepts =
y - intercept =
Domain =
Range =
Shift along x =
Shift along y =
Kind of reflection =
Which statement is grammatically correct?
Question 11 options:
Voy a compro una casa.
Voy a compras una casa.
Ir a compro una casa.
Voy a comprar una casa.
Save
To determine the amplitude, period, x-intercepts, y-intercept, domain, range, shift along x, shift along y, and kind of reflection of the function y = -2sin(x) - 4, let's break it down:
1. Amplitude:
The amplitude represents the maximum distance from the middle value of the function to its highest or lowest point. In this case, the amplitude is the absolute value of the coefficient of the sine function, which is 2. Therefore, the amplitude is 2.
2. Period:
The period represents the length of one complete cycle of the function. For a sine function, the period is determined by the coefficient in front of x. In this case, there is no coefficient other than 1, so the period is 2π. However, since there is no coefficient directly in front of x, we can assume it is 1. Therefore, the period is 2π/1 = 2π.
3. Two x-intercepts:
To find the x-intercepts, we need to set y = 0 and solve for x. So, for the equation -2sin(x) - 4 = 0:
-2sin(x) = 4
sin(x) = -2
Since the range of the sine function is -1 to 1, there are no real solutions for sin(x) = -2. Therefore, the function y = -2sin(x) - 4 does not have any x-intercepts.
4. y-intercept:
To find the y-intercept, we need to set x = 0 and solve for y. So, for x = 0:
y = -2sin(0) - 4
y = -2(0) - 4
y = -4
Therefore, the y-intercept is (0, -4).
5. Domain:
The domain represents the set of all input values (x-values) for which the function is defined. In the case of a sine function, the domain is all real numbers. Therefore, the domain of y = -2sin(x) - 4 is (-∞, ∞).
6. Range:
The range represents the set of all output values (y-values) that the function can produce. For a sine function, the range is between -1 and 1 inclusive, multiplied by the amplitude (2 in this case), and then shifted downward by the y-shift (-4 in this case). Therefore, the range of y = -2sin(x) - 4 is [-6, -2].
7. Shift along x:
To determine the shift along the x-axis, we need to examine the function. In this case, there is no addition or subtraction involving x, indicating that there is no shift along the x-axis. Therefore, the shift along x is 0.
8. Shift along y:
The shift along the y-axis is determined by the constant term in the function. In this case, the constant term is -4, indicating a downward shift of 4 units. Therefore, the shift along y is -4.
9. Kind of reflection:
The reflection of a function can be determined by the coefficient in front of the sine function. In this case, the coefficient is -2, indicating a vertical reflection. Since the coefficient is negative, the reflection is downward.
Summary:
- Amplitude = 2
- Period = 2π
- Two x-intercepts = None
- y-intercept = (0, -4)
- Domain = (-∞, ∞)
- Range = [-6, -2]
- Shift along x = 0
- Shift along y = -4
- Kind of reflection = Downward vertical reflection