Solve for d.
2 answers:
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Answer:
Step-by-step explanation:
Let's start with the simple ones:
a = amplitude = (highest - lowest) divided by 2 = (11-1)/2 = 5
d = offset = (highest + lowest) divided by 2 = (11+1)/2 = 6
Now, if x goes 'untreated', the cos would make a full swing after 2pi.
Here, it repeats after 3. To achieve that, we divide by 3 and multiply by 2pi.
b = 2pi/3
You can try it out (assuming c=0 for a minute): x=3 puts bx at 2pi.
Now for the final one, the shift left by one. We cannot say c=1 because that would be a 1 on the 2pi scale.
Rather, the shift would be c'=1 if the formula were acos(b(x+c')).
If we work out the parenthesis with c'=1, we get bx + b, so the actual c is 2pi/3
The correct answer is shown in attached figure
To find the correct graph, we should study the continuity of the function
Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2
Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3
From the previous results the correct graph is the last as shown in attached graph.
To find the correct graph, we should study the continuity of the function
Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2
Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3
From the previous results the correct graph is the last as shown in attached graph.