y=xy = xy=xIntersection of two linesThe line through two pointsThe distance from a point to a lineParallel and perpendicular linesThe distance between two pointsInternal and external division pointsPerpendicular bisectory=x2y = x^2y=x2Intersection of a quadratic function and a lineIntersection of two quadratic functionsThe vertex of a parabola and completing the squareIntersection of a quadratic function and the x-axisQuadratic inequalitiesMaximum and minimum of a quadratic functionTangent line to a parabolaIntersection of a circle and a parabolaDiscriminant and x-axis intersectionsTranslating a parabolaParabola through three pointsFocus and directrix of a parabolay=x3y = x^3y=x3y=x4y = x^4y=x4y=x5y = x^5y=x5y=x3−3xy = x^3 - 3xy=x3−3xy=x2(x−1)y = x^2(x-1)y=x2(x−1)y=x4−x2y = x^4 - x^2y=x4−x2y=1xy = \dfrac{1}{x}y=x1​y=1x2y = \dfrac{1}{x^2}y=x21​y=11+x2y = \dfrac{1}{1+x^2}y=1+x21​y=x1+x2y = \dfrac{x}{1+x^2}y=1+x2x​y=1x3y = \dfrac{1}{x^3}y=x31​y=1x2−1y = \dfrac{1}{x^2-1}y=x2−11​y=x+1x−1y = \dfrac{x+1}{x-1}y=x−1x+1​y=x+1xy = x + \dfrac{1}{x}y=x+x1​Intersection of a reciprocal function and a lineTranslating a reciprocaly=xy = \sqrt{x}y=x​y=x3y = \sqrt[3]{x}y=3x​y=1−x2y = \sqrt{1 - x^2}y=1−x2​y=x2/3y = x^{2/3}y=x2/3y=x4y = \sqrt[4]{x}y=4x​y=∣x∣y = \sqrt{|x|}y=∣x∣​y=x2+1y = \sqrt{x^2+1}y=x2+1​y=(1−∣x∣2/3)3/2y = \left(1 - |x|^{2/3}\right)^{3/2}y=(1−∣x∣2/3)3/2y=x31−xy = \sqrt{\dfrac{x^3}{1-x}}y=1−xx3​​y=ln⁡1+1−x2x−1−x2y = \ln\dfrac{1+\sqrt{1-x^2}}{x} - \sqrt{1-x^2}y=lnx1+1−x2​​−1−x2​y=x2−1y = \sqrt{x^2-1}y=x2−1​y=x5y = \sqrt[5]{x}y=5x​The equation of a circleIntersection of a circle and a lineIntersection of two circlesThe tangent line to a circlePosition of a point relative to a circleGeneral and standard form of a circleCircle through three pointsTwo tangent circlesCircle tangent to the x-axisy=∣x∣y = |x|y=∣x∣y=x∣x∣y = x|x|y=x∣x∣Intersection of an absolute-value graph and a lineAbsolute value equationParabola with absolute valueSum of two absolute valuesy=2xy = 2^xy=2xy=exy = e^xy=exy=ln⁡xy = \ln xy=lnxy=log⁡10xy = \log_{10} xy=log10​xy=e−xy = e^{-x}y=e−xy=log⁡2xy = \log_2 xy=log2​xy=xe−xy = x e^{-x}y=xe−xy=ln⁡(1+ex)y = \ln(1+e^x)y=ln(1+ex)y=xln⁡xy = x \ln xy=xlnxy=ln⁡xxy = \dfrac{\ln x}{x}y=xlnx​y=exxy = \dfrac{e^x}{x}y=xex​y=xxy = x^xy=xxy=ex−xy = e^x - xy=ex−xy=ln⁡∣x∣y = \ln|x|y=ln∣x∣y=ln⁡x1−xy = \ln\dfrac{x}{1-x}y=ln1−xx​y=xln⁡xy = \dfrac{x}{\ln x}y=lnxx​y=(1+1x)xy = \left(1 + \dfrac{1}{x}\right)^{x}y=(1+x1​)xy=e−1/x2y = e^{-1/x^2}y=e−1/x2Symmetry of exponential and logarithmic functionsIntersection of an exponential function and a lineIntersection of a logarithm and a lineExponential growth and decayLogarithms with different basesy=sin⁡xy = \sin xy=sinxy=cos⁡xy = \cos xy=cosxy=tan⁡xy = \tan xy=tanxy=arcsin⁡xy = \arcsin xy=arcsinxy=arccos⁡xy = \arccos xy=arccosxy=arctan⁡xy = \arctan xy=arctanxy=sec⁡xy = \sec xy=secxy=csc⁡xy = \csc xy=cscxy=cot⁡xy = \cot xy=cotxy=sin⁡xxy = \dfrac{\sin x}{x}y=xsinx​y=xsin⁡xy = x \sin xy=xsinxy=∣sin⁡x∣y = |\sin x|y=∣sinx∣y=x+sin⁡xy = x + \sin xy=x+sinxy=arctan⁡1xy = \arctan\dfrac{1}{x}y=arctanx1​y=sin⁡1xy = \sin\dfrac{1}{x}y=sinx1​y=xsin⁡1xy = x\sin\dfrac{1}{x}y=xsinx1​y=arcsec⁡xy = \operatorname{arcsec} xy=arcsecxy=arccsc⁡xy = \operatorname{arccsc} xy=arccscxy=arccot⁡xy = \operatorname{arccot} xy=arccotxy=sin⁡2xy = \sin^2 xy=sin2xy=sin⁡x+cos⁡xy = \sin x + \cos xy=sinx+cosxy=sin⁡(x2)y = \sin(x^2)y=sin(x2)y=max⁡(sin⁡x, cos⁡x)y = \max(\sin x,\, \cos x)y=max(sinx,cosx)Intersection of a trigonometric function and a lineThe relationship between sine and cosineIntersection of sine and cosineCombining sine and cosineAmplitude and periody=sinh⁡xy = \sinh xy=sinhxy=cosh⁡xy = \cosh xy=coshxy=tanh⁡xy = \tanh xy=tanhxy=sech⁡xy = \operatorname{sech} xy=sechxy=coth⁡xy = \coth xy=cothxy=arsinh⁡xy = \operatorname{arsinh} xy=arsinhxy=arcosh⁡xy = \operatorname{arcosh} xy=arcoshxy=artanh⁡xy = \operatorname{artanh} xy=artanhxy=sech⁡2xy = \operatorname{sech}^2 xy=sech2xy=gd⁡x=arcsin⁡(tanh⁡x)y = \operatorname{gd} x = \arcsin(\tanh x)y=gdx=arcsin(tanhx)y=csch⁡xy = \operatorname{csch} xy=cschxy=arcoth⁡xy = \operatorname{arcoth} xy=arcothxy=arsech⁡xy = \operatorname{arsech} xy=arsechxy=arcsch⁡xy = \operatorname{arcsch} xy=arcschxy=sinh⁡xxy = \dfrac{\sinh x}{x}y=xsinhx​y=⌊x⌋y = \lfloor x \rfloory=⌊x⌋y=sgn⁡(sin⁡x)y = \operatorname{sgn}(\sin x)y=sgn(sinx)y=⌈x⌉y = \lceil x \rceily=⌈x⌉y=round⁡(x)y = \operatorname{round}(x)y=round(x)y=sgn⁡xy = \operatorname{sgn} xy=sgnxy=x−⌊x⌋y = x - \lfloor x \rfloory=x−⌊x⌋y=arcsin⁡(sin⁡x)y = \arcsin(\sin x)y=arcsin(sinx)y=max⁡(0, x)y = \max(0,\,x)y=max(0,x)y=e−x2y = e^{-x^2}y=e−x2y=11+e−xy = \dfrac{1}{1+e^{-x}}y=1+e−x1​y=erf⁡xy = \operatorname{erf} xy=erfxy=Γ(x)y = \Gamma(x)y=Γ(x)y=e−xsin⁡xy = e^{-x}\sin xy=e−xsinxy=e−∣x∣y = e^{-|x|}y=e−∣x∣y=Φ(x)=12(1+erf⁡x2)y = \Phi(x) = \dfrac{1}{2}\left(1 + \operatorname{erf}\dfrac{x}{\sqrt{2}}\right)y=Φ(x)=21​(1+erf2​x​)y=ln⁡Γ(x)y = \ln \Gamma(x)y=lnΓ(x)y=xe−x2y = xe^{-x^2}y=xe−x2y=sin⁡x+sin⁡2x2+sin⁡3x3y = \sin x + \dfrac{\sin 2x}{2} + \dfrac{\sin 3x}{3}y=sinx+2sin2x​+3sin3x​The area of a triangle in the coordinate planeCentroid of a triangleTriangle bounded by three linesFourth vertex of a parallelogramIncircle of a triangleCircumcircle of a triangleOrthocenter of a triangleThe area of a polygon and the shoelace formulaThe area of a trapezoidCyclic quadrilateralsRight triangles and the Pythagorean theoremThe regular hexagonAverage rate of change and the derivative at a pointThe derivative and the tangent lineThe graph of the derivative and its signThe sign table and the shape of the graphInflection points and concavityLocal extrema versus maximum and minimumThe mean value theoremNewton's methodPoints where a function is not differentiableThe product ruleThe quotient ruleThe chain ruleDerivatives of the exponential and the logarithmDerivatives of the trigonometric functionsLinear approximationImplicit differentiationProving inequalities with derivativesThe definite integral and areaRiemann sumsThe area between two curvesThe area enclosed by a parabola and a lineSigned area and absolute valuesThe fundamental theorem of calculusThe average value of a functionImproper integralsDefinite integrals of trigonometric functionsIntegration by substitutionIntegration by partsThe volume of a solid of revolutionThe volume of a coneThe length of a curveDefining the logarithm as an areaDefinite integrals of the exponentialThe trapezoidal rule