Graphing y = (x-2)*cos(x)-1

In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} =$$
the first derivative
$$- \left(x - 2\right) \sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
Solve this equation
The roots of this equation
$$x_{1} = 31.4498695022248$$
$$x_{2} = 3.67881386877315$$
$$x_{3} = -94.2581679627629$$
$$x_{4} = 81.6939563377856$$
$$x_{5} = 59.707587427833$$
$$x_{6} = -56.565740934319$$
$$x_{7} = -40.8640298498727$$
$$x_{8} = -9.51143060086678$$
$$x_{9} = -65.9881531096995$$
$$x_{10} = 1.78375866918844$$
$$x_{11} = -72.2700945885545$$
$$x_{12} = 62.8482859091507$$
$$x_{13} = -0.395463310223558$$
$$x_{14} = -31.4458167365799$$
$$x_{15} = 9.55635238563905$$
$$x_{16} = 28.3123206099473$$
$$x_{17} = 100.541112615137$$
$$x_{18} = -62.8472726985923$$
$$x_{19} = -53.4251155156868$$
$$x_{20} = -81.6933568044194$$
$$x_{21} = -37.72428004861$$
$$x_{22} = 94.2586182790224$$
$$x_{23} = 37.7270944985589$$
$$x_{24} = -47.1442352627113$$
$$x_{25} = -91.1169257274417$$
$$x_{26} = 40.8664279674596$$
$$x_{27} = -28.307317248383$$
$$x_{28} = -3.3271508114264$$
$$x_{29} = 91.1174076354308$$
$$x_{30} = -69.1290963970556$$
$$x_{31} = 75.4118446237714$$
$$x_{32} = -100.54071682934$$
$$x_{33} = -44.0040309531782$$
$$x_{34} = 44.0060987215772$$
$$x_{35} = -25.1695305580579$$
$$x_{36} = -15.7641969219382$$
$$x_{37} = 78.5528784628996$$
$$x_{38} = -75.4111410048686$$
$$x_{39} = 34.5881955213684$$
$$x_{40} = 72.2708607217157$$
$$x_{41} = 65.9890721217494$$
$$x_{42} = 69.1299337614882$$
$$x_{43} = 47.1460365210195$$
$$x_{44} = -84.8345172956245$$
$$x_{45} = -87.9757079538691$$
$$x_{46} = 56.5669918107247$$
$$x_{47} = 6.50177094567593$$
$$x_{48} = -97.3994323415189$$
$$x_{49} = -22.0327344991331$$
$$x_{50} = -34.5848461068827$$
$$x_{51} = 84.8350732415513$$
$$x_{52} = 53.4265178816223$$
$$x_{53} = -6.40165218273828$$
$$x_{54} = 22.041004922887$$
$$x_{55} = 97.3998540737208$$
$$x_{56} = 25.1758628206516$$
$$x_{57} = -18.8973723517571$$
$$x_{58} = 18.9086285150365$$
$$x_{59} = -50.2846062141866$$
$$x_{60} = 50.2861893528066$$
$$x_{61} = -12.6345957962324$$
$$x_{62} = -59.7064647571766$$
$$x_{63} = 15.7804031090056$$
$$x_{64} = 87.9762248985139$$
$$x_{65} = 12.6599063318801$$
$$x_{66} = -78.5522300076593$$
The values of the extrema at the points:

(31.449869502224804, 28.4329061660693)

(3.6788138687731515, -2.4423261437596)

(-94.25816796276293, -97.2529740187882)

(81.69395633778561, 78.6876830771009)

(59.70758742783301, -58.6989250067643)

(-56.565740934318995, -59.5572053862765)

(-40.86402984987269, 41.8523698171316)

(-9.511430600866776, 10.4682398119322)

(-65.98815310969954, 66.9808000803132)

(1.7837586691884353, -0.954296044655501)

(-72.27009458855454, 73.2633633189962)

(62.84828590915069, 59.840070414946)

(-0.3954633102235576, -3.2105770915696)

(-31.44581673657989, -34.4308771996032)

(9.556352385639048, -8.4910395497374)

(28.312320609947253, -27.2933386654907)

(100.5411126151373, 97.5360389827065)

(-62.84727269859232, -65.8395636489917)

(-53.42511551568677, 54.416096536549)

(-81.69335680441941, -84.6873832541994)

(-37.72428004860999, -40.7116992671584)

(94.25861827902244, 91.2531992086267)

(37.72709449855892, 34.7131077355865)

(-47.144235262711305, 48.1340642877963)

(-91.11692572744167, 92.1115565987741)

(40.86642796745955, -39.8535697780878)

(-28.30731724838301, 29.2908330407422)

(-3.327150811426404, 4.23570188454047)

(91.11740763543084, -90.1117975890844)

(-69.1290963970556, -72.1220679668166)

(75.41184462377139, 72.4050346814387)

(-100.54071682933989, -103.535841065316)

(-44.00403095317819, -46.9931661904766)

(44.00609872157723, 40.99420074504)

(-25.169530558057946, -28.151146266585)

(-15.764196921938192, 16.7361171391436)

(78.55287846289957, -77.5463478656221)

(-75.4111410048686, -78.4046827945409)

(34.58819552136843, -33.5728633693928)

(72.27086072171569, -71.2637464774058)

(65.98907212174937, -64.9812597185053)

(69.1299337614882, 66.1224867587443)

(47.14603652101946, -46.1349654254229)

(-84.83451729562454, 85.8287597894178)

(-87.97570795386915, -90.9701514131668)

(56.56699181072473, 53.5578310694696)

(6.5017709456759265, 3.3946518854198)

(-97.39943234151892, 98.3944025135118)

(-22.032734499133085, 23.0119565195799)

(-34.58484610688265, 35.5711868995092)

(84.83507324155133, -83.8290378107188)

(53.42651788162232, -52.4167980275174)

(-6.401652182738283, -9.34276502535275)

(22.041004922886987, -21.0161025655791)

(97.39985407372076, -96.3946134074225)

(25.175862820651595, 22.1543187289346)

(-18.897372351757102, -21.8734869122759)

(18.908628515036522, 15.8791351607143)

(-50.284606214186574, -53.2750457928642)

(50.286189352806645, 47.2758377548162)

(-12.634595796232404, -15.6005493587407)

(-59.70646475717664, 60.6983634741336)

(15.780403109005595, -14.7442623739808)

(87.97622489851388, 84.9704099272799)

(12.659906331880052, 9.61330893030344)

(-78.55223000765935, 79.5460235722291)

Intervals of increase and decrease of the function:
Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
Minima of the function at points:
$$x_{1} = 3.67881386877315$$
$$x_{2} = -94.2581679627629$$
$$x_{3} = 59.707587427833$$
$$x_{4} = -56.565740934319$$
$$x_{5} = -0.395463310223558$$
$$x_{6} = -31.4458167365799$$
$$x_{7} = 9.55635238563905$$
$$x_{8} = 28.3123206099473$$
$$x_{9} = -62.8472726985923$$
$$x_{10} = -81.6933568044194$$
$$x_{11} = -37.72428004861$$
$$x_{12} = 40.8664279674596$$
$$x_{13} = 91.1174076354308$$
$$x_{14} = -69.1290963970556$$
$$x_{15} = -100.54071682934$$
$$x_{16} = -44.0040309531782$$
$$x_{17} = -25.1695305580579$$
$$x_{18} = 78.5528784628996$$
$$x_{19} = -75.4111410048686$$
$$x_{20} = 34.5881955213684$$
$$x_{21} = 72.2708607217157$$
$$x_{22} = 65.9890721217494$$
$$x_{23} = 47.1460365210195$$
$$x_{24} = -87.9757079538691$$
$$x_{25} = 84.8350732415513$$
$$x_{26} = 53.4265178816223$$
$$x_{27} = -6.40165218273828$$
$$x_{28} = 22.041004922887$$
$$x_{29} = 97.3998540737208$$
$$x_{30} = -18.8973723517571$$
$$x_{31} = -50.2846062141866$$
$$x_{32} = -12.6345957962324$$
$$x_{33} = 15.7804031090056$$
Maxima of the function at points:
$$x_{33} = 31.4498695022248$$
$$x_{33} = 81.6939563377856$$
$$x_{33} = -40.8640298498727$$
$$x_{33} = -9.51143060086678$$
$$x_{33} = -65.9881531096995$$
$$x_{33} = 1.78375866918844$$
$$x_{33} = -72.2700945885545$$
$$x_{33} = 62.8482859091507$$
$$x_{33} = 100.541112615137$$
$$x_{33} = -53.4251155156868$$
$$x_{33} = 94.2586182790224$$
$$x_{33} = 37.7270944985589$$
$$x_{33} = -47.1442352627113$$
$$x_{33} = -91.1169257274417$$
$$x_{33} = -28.307317248383$$
$$x_{33} = -3.3271508114264$$
$$x_{33} = 75.4118446237714$$
$$x_{33} = 44.0060987215772$$
$$x_{33} = -15.7641969219382$$
$$x_{33} = 69.1299337614882$$
$$x_{33} = -84.8345172956245$$
$$x_{33} = 56.5669918107247$$
$$x_{33} = 6.50177094567593$$
$$x_{33} = -97.3994323415189$$
$$x_{33} = -22.0327344991331$$
$$x_{33} = -34.5848461068827$$
$$x_{33} = 25.1758628206516$$
$$x_{33} = 18.9086285150365$$
$$x_{33} = 50.2861893528066$$
$$x_{33} = -59.7064647571766$$
$$x_{33} = 87.9762248985139$$
$$x_{33} = 12.6599063318801$$
$$x_{33} = -78.5522300076593$$
Decreasing at intervals
$$\left[97.3998540737208, \infty\right)$$
Increasing at intervals
$$\left(-\infty, -100.54071682934\right]$$