Respuesta :
Answer:
3 cos((x - π ) - 4 = 3 cos(x) - 4 since cos(x-π) = cos(x)
-1 ≤ cos(x) ≤ 1
-3 ≤ 3cos(x) ≤ 3
-3-4 ≤ 3 cos(x)-4 ≤ 3-4
-7 ≤ 3 cos(x) ≤ -1
The range is -7 to -1 so the midpoint is (-7-1)/2 = -4
y = -4 is the equation of the midline
Step-by-step explanation:
there you go
Answer with explanation:
y=3 Cos (x-π)-4
The Equation of mid line of a function can be obtained by finding the Mean of Maximum and Minimum Value of the function and then finding the equation of line passing through that point.
→Cos (x-π)=Cos[-(π-x)]= -Cos x, Cos (-x)=Cos x,and,Cos(π-x)= -Cos x,as Cos x is Negative in Second Quadrant.
The above function can be written as
y= -3 Cos x -4
→ -1 ≤ Cos x ≤ 1
→ -3≤-3 Cos x≤3
→ -3 -4≤ -3 Cos x -4≤3-4
→ -7 ≤ -3 Cos x -4 ≤ -1
The Maximum Value of the function , 3 Cos (x-pi)-4, is -1, and Minimum value of the function is ,-7.
Mean of Maximum and Minimum is
[tex]=\frac{-1+-7}{2}=\frac{-8}{2}= -4[/tex]
→Equation of mid line of the function, y=3 Cos (x-pi)-4, is
y = -4
