Sketch the curve y = x3 + x. | Mathematics I 2074

Mathematics I20745 marksNumerical: curve sketchingCurve sketching

Sketch the curve $y = x^3 + x$ . [5]

Sketch the curve $y = x^3 + x$. [5]

As a polynomial, the domain is all real numbers $(-\infty, \infty)$ . Since it is strictly increasing (shown below) and unbounded, the range is also $(-\infty, \infty)$ . x-intercept (set $y=0$ ): $x^3 + x = 0 \implies x(x^2+1) = 0$ Since $x^2 + 1 0$ , the only real solution is $x = 0$ . y-intercept...

As a polynomial, the domain is all real numbers $(-\infty, \infty)$. Since it is strictly increasing (shown below) and unbounded, the range is also $(-\infty, \infty)$. x-intercept (set $y=0$): $$x^3 + x = 0 \implies x(x^2+1) = 0$$ Since $x^2 + 1 0$, the only real solution is $x = 0$. y-intercept...

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