y=xy = xy=x二直線の交点二点を通る直線点と直線の距離平行な直線と垂直な直線二点間の距離内分点と外分点垂直二等分線y=x2y = x^2y=x2二次関数と直線の交点二次関数どうしの交点放物線の頂点と平方完成二次関数と x 軸の交点二次不等式二次関数の最大・最小放物線の接線円と放物線の交点判別式と共有点の個数放物線の平行移動三点を通る放物線放物線の焦点と準線y=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​反比例と直線の交点分数関数のグラフy=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​円の方程式円と直線の交点円と円の交点円の接線点と円の位置関係円の一般形と標準形三点を通る円2つの円が接するx軸に接する円y=∣x∣y = |x|y=∣x∣y=x∣x∣y = x|x|y=x∣x∣絶対値のグラフと直線の交点絶対値の方程式絶対値をつけた放物線絶対値の和のグラフy=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/x2指数関数と対数関数の対称性指数関数と直線の交点対数関数と直線の交点指数関数の増加と減衰対数関数と底y=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)三角関数と直線の交点sin と cos の関係sin と cos の交点三角関数の合成三角関数の振幅と周期y=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​座標平面上の三角形の面積三角形の重心三直線で囲まれた三角形平行四辺形の第4頂点三角形の内接円三角形の外接円三角形の垂心多角形の面積とシューレースの公式台形の面積円に内接する四角形直角三角形とピタゴラスの定理正六角形平均変化率と微分係数導関数と接線導関数のグラフと符号増減表とグラフの形変曲点と凹凸極値と最大・最小の違い平均値の定理ニュートン法微分できない点積の微分商の微分合成関数の微分指数関数と対数関数の微分三角関数の微分一次近似陰関数の微分微分で示す不等式定積分と面積区分求積法2 曲線で囲む面積放物線と直線が囲む面積符号つき面積と絶対値微分積分学の基本定理関数の平均値広義積分三角関数の定積分置換積分部分積分回転体の体積円錐の体積曲線の長さ対数を面積で定義する指数関数の定積分台形公式