Mister Exam

Other calculators

Plotting a function graph/ tg3x+1

Graphing y = tg3x+1

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = tan(3*x) + 1
f(x)=tan⁡(3x)+1f{\left(x \right)} = \tan{\left(3 x \right)} + 1 
f = tan(3*x) + 1
The graph of the function
02468-8-6-4-2-1010-250250
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
tan⁡(3x)+1=0\tan{\left(3 x \right)} + 1 = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=−π12x_{1} = - \frac{\pi}{12}
Numerical solution
x1=61.5228561328001x_{1} = 61.5228561328001
x2=−72.5184304203644x_{2} = -72.5184304203644
x3=−2.35619449019234x_{3} = -2.35619449019234
x4=41.6261026600648x_{4} = 41.6261026600648
x5=−84.037603483527x_{5} = -84.037603483527
x6=80.3724120543389x_{6} = 80.3724120543389
x7=−96.6039740978861x_{7} = -96.6039740978861
x8=34.2957198016886x_{8} = 34.2957198016886
x9=−55.7632696012188x_{9} = -55.7632696012188
x10=−22.2529479629277x_{10} = -22.2529479629277
x11=30.1069295969022x_{11} = 30.1069295969022
x12=93.9859802198946x_{12} = 93.9859802198946
x13=87.7027949127151x_{13} = 87.7027949127151
x14=−29.5833308213039x_{14} = -29.5833308213039
x15=39.5317075576716x_{15} = 39.5317075576716
x16=−15.9697626557481x_{16} = -15.9697626557481
x17=−11.7809724509617x_{17} = -11.7809724509617
x18=−9.68657734856853x_{18} = -9.68657734856853
x19=78.2780169519457x_{19} = 78.2780169519457
x20=76.1836218495525x_{20} = 76.1836218495525
x21=−31.6777259236971x_{21} = -31.6777259236971
x22=23.8237442897226x_{22} = 23.8237442897226
x23=36.3901149040818x_{23} = 36.3901149040818
x24=−77.7544181763474x_{24} = -77.7544181763474
x25=−50.5272818452358x_{25} = -50.5272818452358
x26=69.9004365423729x_{26} = 69.9004365423729
x27=32.2013246992954x_{27} = 32.2013246992954
x28=−51.5744793964324x_{28} = -51.5744793964324
x29=37.4373124552784x_{29} = 37.4373124552784
x30=−48.4328867428426x_{30} = -48.4328867428426
x31=14.3989663289532x_{31} = 14.3989663289532
x32=74.0892267471593x_{32} = 74.0892267471593
x33=−75.6600230739542x_{33} = -75.6600230739542
x34=83.5140047079287x_{34} = 83.5140047079287
x35=56.2868683768171x_{35} = 56.2868683768171
x36=63.6172512351933x_{36} = 63.6172512351933
x37=−18.0641577581413x_{37} = -18.0641577581413
x38=−62.0464549083984x_{38} = -62.0464549083984
x39=−73.565627971561x_{39} = -73.565627971561
x40=15.4461638801498x_{40} = 15.4461638801498
x41=−7.59218224617533x_{41} = -7.59218224617533
x42=28.012534494509x_{42} = 28.012534494509
x43=−37.9609112308767x_{43} = -37.9609112308767
x44=−97.6511716490827x_{44} = -97.6511716490827
x45=12.30457122656x_{45} = 12.30457122656
x46=47.9092879672443x_{46} = 47.9092879672443
x47=67.8060414399797x_{47} = 67.8060414399797
x48=−26.4417381677141x_{48} = -26.4417381677141
x49=−44.2440965380563x_{49} = -44.2440965380563
x50=54.1924732744239x_{50} = 54.1924732744239
x51=−64.1408500107916x_{51} = -64.1408500107916
x52=−86.1319985859202x_{52} = -86.1319985859202
x53=−13.8753675533549x_{53} = -13.8753675533549
x54=−0.261799387799149x_{54} = -0.261799387799149
x55=19.6349540849362x_{55} = 19.6349540849362
x56=85.6083998103219x_{56} = 85.6083998103219
x57=−59.9520598060052x_{57} = -59.9520598060052
x58=−66.2352451131848x_{58} = -66.2352451131848
x59=−28.5361332701073x_{59} = -28.5361332701073
x60=−68.329640215578x_{60} = -68.329640215578
x61=−70.4240353179712x_{61} = -70.4240353179712
x62=21.7293491873294x_{62} = 21.7293491873294
x63=−20.1585528605345x_{63} = -20.1585528605345
x64=3.92699081698724x_{64} = 3.92699081698724
x65=−79.8488132787406x_{65} = -79.8488132787406
x66=−4.45058959258554x_{66} = -4.45058959258554
x67=−35.8665161284835x_{67} = -35.8665161284835
x68=10.2101761241668x_{68} = 10.2101761241668
x69=59.4284610304069x_{69} = 59.4284610304069
x70=45.8148928648512x_{70} = 45.8148928648512
x71=100.269165527074x_{71} = 100.269165527074
x72=8.11578102177363x_{72} = 8.11578102177363
x73=−88.2263936883134x_{73} = -88.2263936883134
x74=−33.7721210260903x_{74} = -33.7721210260903
x75=89.7971900151083x_{75} = 89.7971900151083
x76=−92.4151838930998x_{76} = -92.4151838930998
x77=43.720497762458x_{77} = 43.720497762458
x78=17.540558982543x_{78} = 17.540558982543
x79=71.9948316447661x_{79} = 71.9948316447661
x80=−57.857664703612x_{80} = -57.857664703612
x81=−46.3384916404494x_{81} = -46.3384916404494
x82=−53.6688744988256x_{82} = -53.6688744988256
x83=96.0803753222878x_{83} = 96.0803753222878
x84=25.9181393921158x_{84} = 25.9181393921158
x85=−24.3473430653209x_{85} = -24.3473430653209
x86=91.8915851175014x_{86} = 91.8915851175014
x87=−90.3207887907066x_{87} = -90.3207887907066
x88=52.0980781720307x_{88} = 52.0980781720307
x89=−40.0553063332699x_{89} = -40.0553063332699
x90=98.174770424681x_{90} = 98.174770424681
x91=58.3812634792103x_{91} = 58.3812634792103
x92=−81.9432083811338x_{92} = -81.9432083811338
x93=81.4196096055355x_{93} = 81.4196096055355
x94=−94.5095789954929x_{94} = -94.5095789954929
x95=1.83259571459405x_{95} = 1.83259571459405
x96=−42.1497014356631x_{96} = -42.1497014356631
x97=−6.54498469497874x_{97} = -6.54498469497874
x98=65.7116463375865x_{98} = 65.7116463375865
x99=50.0036830696375x_{99} = 50.0036830696375
x100=6.02138591938044x_{100} = 6.02138591938044
x101=−99.7455667514759x_{101} = -99.7455667514759
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to tan(3*x) + 1.
tan⁡(0⋅3)+1\tan{\left(0 \cdot 3 \right)} + 1
The result:
f(0)=1f{\left(0 \right)} = 1
The point:
(0, 1)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
3tan⁡2(3x)+3=03 \tan^{2}{\left(3 x \right)} + 3 = 0
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
18(tan⁡2(3x)+1)tan⁡(3x)=018 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} = 0
Solve this equation
The roots of this equation
x1=0x_{1} = 0

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
[0,∞)\left[0, \infty\right)
Convex at the intervals
(−∞,0]\left(-\infty, 0\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=lim⁡x→−∞(tan⁡(3x)+1)y = \lim_{x \to -\infty}\left(\tan{\left(3 x \right)} + 1\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞(tan⁡(3x)+1)y = \lim_{x \to \infty}\left(\tan{\left(3 x \right)} + 1\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of tan(3*x) + 1, divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
y=xlim⁡x→−∞(tan⁡(3x)+1x)y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(3 x \right)} + 1}{x}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(tan⁡(3x)+1x)y = x \lim_{x \to \infty}\left(\frac{\tan{\left(3 x \right)} + 1}{x}\right)
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
tan⁡(3x)+1=1−tan⁡(3x)\tan{\left(3 x \right)} + 1 = 1 - \tan{\left(3 x \right)}
- No
tan⁡(3x)+1=tan⁡(3x)−1\tan{\left(3 x \right)} + 1 = \tan{\left(3 x \right)} - 1
- No
so, the function
not is
neither even, nor odd
    © Mister Exam – Calculator