Practice section 2 of 6

Find the coordinates of the turning points of the curve $y=(x^2-3x)/(x+1)$, indicating the nature of each turning point.

Find the range of values of $x$ and $y$ for the following curves:

(a) $y=\ln(x-3)$.

(b) $y=-\sqrt{3-x}$.

(c) $y=(x^2+2)/(x+1)$.

Sketch the following curves, indicating clearly the coordinates of any intersections with the axes and turning points:

(a) $y=(x+1)(x-1)^4$.

(b) $y=(x+1)^2(x-1)^3$.

A cubic polynomial curve, $C$, is shown below, find a possible equation for $C$.

Sketch the graph of the following curves, indicating clearly the coordinates of any intersections with the axes, turning points and the equations of any asymptotes:

(a) $y=e^x(x-1)$.

(b) $y=\dfrac{e^x-1}{e^{2x}+1}$.

Sketch the graph of the following curves, indicating clearly the coordinates of any intersections with the axes, turning points and the equations of any asymptotes:

(a) $y=\dfrac{2x-3}{x-4}$.

(b) $y=\dfrac{x^2-2}{x^2-1}$.

(c) $y=\dfrac{2x^2-x+1}{x-2}$.

(d) $y=\dfrac{x^2-x-12}{x-2}$.

(e) $y=\dfrac{(x+5)^2}{x^2-5x}$.