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Question Number 35645 by mondodotto@gmail.com last updated on 21/May/18

$$\mathbf{sketch}\mathbf{the}\mathbf{graph}\mathbf{of}$$$$\mathbf{f}\left(\mathit{x}\right)=2-\mathit{x}-{\mathit{x}}^2$$$$\mathbf{then}\mathbf{state}\mathbf{its}\mathbf{domain}\mathbf{and}\mathbf{range}$$

Answered by Penguin last updated on 21/May/18

$$\mathrm{Domain}:$$$$x\in [-\mathrm{\infty },\mathrm{\infty }]$$$$$$$$\mathrm{Range}:$$$$\mathrm{Max}\min y@y^{\prime }=0$$$$y^{\prime }=-1-2x=0$$$$x=-\frac{1}{2}$$$$y=2-(-\frac{1}{2})-{(-\frac{1}{2})}^2$$$$y=2+\frac{1}{2}-\frac{1}{4}$$$$y=\frac{9}{4}$$$$$$$$\max /\min ?$$$$y^{″}=-2$$$$\therefore \mathrm{Maximum}$$$$$$$$\therefore y\in [-\mathrm{\infty },\frac{9}{4}]$$

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