The function in the graph has the general equation f(x)=asin(bx+c)+d. Which of the following values are correct? Select all that apply
d=-3
C=-1
B=0.5
B=0.5
D=1
A=2
B=2
1. B (f(x)=4cos(x/2)-3)
2. B,F,G (c=-1; a=2; b=2)
3. C (H(t)=-2.4cos(0.017t))
4. A,B,E,F (y=cos^-1x; y=cot^-1x; y=sin^-1x; y=tan^-1x)
5. C (y=sin^-1x)
6. C (48.7°)
7. C (f(g(x))=sec(sinx); domain: all real numbers; range: 1 <= x <=1.85
8. C (step 3)
c = -1
a = 2
b = 2
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To determine which values are correct, let's analyze the general equation of the function. The equation given is f(x) = asin(bx + c) + d.
Looking at the variables in the equation:
- a represents the amplitude of the function.
- b controls the frequency of the function.
- c represents the horizontal shift of the function.
- d represents the vertical shift of the function.
Let's go through each option and see if it matches with the given general equation:
Option A: A = 2
This value represents the amplitude of the function. It does not appear in the general equation, so it is not correct.
Option B: B = 0.5
This value represents the value of b, which controls the frequency of the function. It is mentioned twice in the options, but the variable b is not mentioned in the general equation. Therefore, it is not correct.
Option C: C = -1
This value represents the value of c, which represents the horizontal shift of the function. It is mentioned in the general equation, so it is correct.
Option D: D = 1
This value represents the value of d, which represents the vertical shift of the function. It is mentioned in the general equation, so it is correct.
Option E: B = 2
As mentioned earlier, the variable b is not present in the general equation, so this value is not correct.
Option F: d = -3
This value represents the value of d, which represents the vertical shift of the function. It is mentioned in the general equation, so it is correct.
In conclusion, the correct values are:
- C = -1
- D = 1
- d = -3
Therefore, options C, D, and F are correct.