As we have y=2+12sin2(x−5) and any sine ratio has maximum value of +1 and minimum value of −1,
maximum value of y will be 2+12=212 and minimum value will be 2−12=112. As such there is no x-intercept.
Hence y will move between these two numbers.
Maxima 212 is there when 2(x−5)=4n+12π i.e. at x=4n+14π+5=nπ+π4+5 and some values are x={−0.4978,2.6438,5.7854,8.927,12.0686}
Minima 112 is there when 2(x−5)=4n−12π i.e. at x=4n−14π+5=nπ−π4+5 and some values are x={−2.0686,1.073,4.2146,7.3562,10.4978}
Mean value 2 appears at 2(x−5)=nπ i.e. x=n2π+5 and some values are x={0.2876,1.8584,3.4292,5,6.5708,8.1416,9.7124}
Now when x=0, we have y=2+12×sin(−5) ad considering it in radiansm y=2+12×0.9589=2.4795 and hence y intercept is ≅2.48
and function appears as follows
graph{2+(1/2)sin(2x-10) [-1.46, 8.54, -0.58, 4.42]}
