i'm uncertain why you're able to need a graphing calculator, yet i'm going to do it the two techniques for you. devoid of a graphing calculator: comprehend that sine maximizes at one million and minimizes at -one million. replace sin(4x + 80) with one million for the optimum and sin(4x + 80) with -one million for the minimum. optimum: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(one million) + 7.3 = 12.5 minimum: f(x) = 5.2sin(4x + 80) + 7.3 = 5.2(-one million) + 7.3 = 2.one million hence, the optimum fee is 12.5 and minimum fee is two.one million. With a graphing calculator: i'm going to tutor you the stairs that i could use on my TI-80 4 Plus Silver version. maximum human beings in Precalc have comparable calculators so it (or some version of those steps) ought to paintings for you. Step one million: pass to "Y=" and form in 5.2sin(4x + 80) + 7.3 for "Y1=" on the suitable. Step 2: pass to "WINDOW." replace the window so the graph is actual viewable. From what we discovered above, replace "Xmin = 0" and "Xmax = 5". replace "Ymin = one million.5" and Ymax" = 13." The x values do no longer remember in any respect, certainly, however the y values accomplish that the optimum and minimum values would be seen. Step 3: Press "GRAPH." Step 4: After that's complete graphing, press "2nd," then "CALC" (that's on the "hint" button). Press "3: minimum" first. as quickly as you place the limits between a minimum dip, this is going to tutor the linked fee "Y=2.one million," which confirms our answer above. Step 5: further, press "2nd," then "CALC" returned. Press "4: optimum" this time. as quickly as you place the limits between a optimum top, this is going to tutor the linked fee "Y=12.5," which additionally confirms our answer. observe that it became right into a lot greater handy to clean up it devoid of graphing by means of utilising noticing that sine maximizes at one million and minimizes at -one million.