What is the domain and range of $y = - 2 x^{2} + 1$ $y=-2x^2+1$ ?

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Answer 1 · 2018-04-17T21:38:39

Since there are no roots or fractions, the domain is unlimited:
$- \infty < x < + \infty$ $- oo < x< +oo$

The smallest value of $x^{2}$ $x^2$ can be $0$ $0$ or $x^{2} \geq 0$ $x^2>=0$

Which means that $- 2 x^{2} \leq 0 \to - 2 x^{2} + 1 \leq 1$ $-2x^2<=0->-2x^2+1<=1$

Which puts the range as: $- \infty < y \leq 1$ $- oo < y <=1$
graph{-2x^2+1 [-10, 10, -5, 5]}

What is the domain and range of y=−2x2+1y=-2x^2+1 ?