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# [原创] 欣赏一些函数图象

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https://www.desmos.com/calculator/dj7vjfsj6s?lang=zh-CN

楼主| 发表于 2021-10-5 21:27:05 | 显示全部楼层
 函数$$y=x^2$$ https://www.desmos.com/calculator/13on7bph8f

楼主| 发表于 2021-10-5 21:27:34 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 22:38 编辑 函数$$y=x^3$$和$$y=Ax^3$$ https://www.desmos.com/calculator/bvjzo3eh34

楼主| 发表于 2021-10-5 21:28:27 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 22:48 编辑 函数$$y=x^5$$和$$y=(Ax+B)^5$$ https://www.desmos.com/calculator/rxlnnsslq0 函数$$y=x^e$$ https://www.desmos.com/calculator/geabxblici 函数$$\D y=\frac{1}{x^{2}}$$和$$\D y=\frac{1}{x^{3}}$$和$$\D y=\frac{1}{x^{5}}$$ https://www.desmos.com/calculator/horbfwrqht

楼主| 发表于 2021-10-5 21:29:41 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-6 00:33 编辑 双曲线 $$\D xy=t\ \implies y=\frac{t}{x}$$ $$\D (x+a)y=t \implies y=\frac{t}{x+a}$$ $$\D (x+a)(y+b)=xy+bx+ay+ab=t \implies y=\frac{t-ab-bx}{x+a}\$$ https://www.desmos.com/calculator/xoopyshebs $$\D y=\frac{x^{2}}{ax+b}$$ https://www.desmos.com/calculator/z8daqz7x4q $$\D y=\frac{t}{ax+b}$$ $$\D \implies a(x+\frac{b}{a})y=t$$ $$\D \implies y=\frac{\D \frac{t}{a}}{\D x+\frac{b}{a}}$$ https://www.desmos.com/calculator/gyk4kzswue $$\D y=\frac{x}{ax+b}$$ $$\D \implies a(ax+b)y=ax$$ $$\D \implies a(ax+b)y+b=ax+b$$ $$\D \implies (ay-1)(ax+b)+b=0$$ $$\D \implies (y-\frac{1}{a})(x+\frac{b}{a})=\frac{-b}{a^2}$$ https://www.desmos.com/calculator/466zvkho5g $$\D y=\sqrt{x^{2}+a^{2}}$$ $$\implies y^{2}-x^{2}=a^{2}$$ https://www.desmos.com/calculator/5bmz3iewxk $$\D y=\sqrt{x^{2}-a^{2}}$$ $$\implies x^{2}-y^{2}=a^{2}$$ https://www.desmos.com/calculator/cu8rtah1ac

楼主| 发表于 2021-10-5 21:35:04 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 22:56 编辑 $$\D y=\frac{1}{x^{2}\left(ax+b\right)}$$ https://www.desmos.com/calculator/mi97vkzrwp

楼主| 发表于 2021-10-5 22:10:42 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-6 01:19 编辑 $$\D (ax^2+bx+c)y=t \implies \D y=\frac{t}{ax^2+bx+c}$$ $$\D \implies (4a^2x^2+4abx+4ac)y=4at$$ $$\D \implies (2ax+b)^2+(4ac-b^2)=\frac{4at}{y}$$ $$\D \implies 4a^2(x+\frac{b}{2a})^2+(4ac-b^2)=\frac{4at}{y}$$ $$\D \implies (x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a^2}=\frac{t}{ay}$$ $$\D \implies y=\frac{\D \frac{t}{a}}{\D (x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a^2}}$$ https://www.desmos.com/calculator/hd78xfykwl https://www.desmos.com/calculator/pnk76ijkxd https://www.desmos.com/calculator/v5yrhutnbj $$\D y=\sqrt{\frac{x-a}{x-b}}$$ $$\left(x-b\right)y^{2}=x-a$$ $$xy^2-by^2=x-a$$ $$x(y^2-1)=by^2-a$$ $$x(y^2-1)=by^2-b+b-a$$ $$x(y^2-1)=b(y^2-1)+b-a$$ $$(x-b)(y^2-1)=b-a$$ https://www.desmos.com/calculator/7urca6snua $$\D y=\sqrt{\frac{x-a}{b-x}}$$ $$y^2(b-x)=x-a$$ $$by^2-xy^2=x-a$$ $$x(y^2+1)=by^2+a$$ $$x(y^2+1)=by^2+b-b+a$$ $$x(y^2+1)=b(y^2+1)-b+a$$ $$(x-b)(y^2+1)=a-b$$ https://www.desmos.com/calculator/em1zz5owdo

楼主| 发表于 2021-10-5 22:26:31 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 23:03 编辑 $$\D y=\frac{x}{\left(ax+b\right)^{2}}$$ https://www.desmos.com/calculator/axgp3xzdge

楼主| 发表于 2021-10-5 22:28:29 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 23:05 编辑 $$\D y=\frac{x^{2}}{\left(ax+b\right)^{2}}$$ https://www.desmos.com/calculator/ojudqajifu

楼主| 发表于 2021-10-5 22:29:32 | 显示全部楼层
 本帖最后由 manthanein 于 2021-10-5 23:06 编辑 $$\D y=\frac{1}{x\left(ax+b\right)^{2}}$$ https://www.desmos.com/calculator/ftrjwemsj1

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