DP Mathematics: Analysis and Approaches Questionbank

Solve the inequality $0<\frac{2\left|x\right|-1}{\left|x\right|+1}<2$.

Sketch the curve $y=f\left(x\right)$, clearly indicating any asymptotes with their equations. State the coordinates of any local maximum or minimum points and any points of intersection with the coordinate axes.

The following diagram shows the graph of $y=f\left(x\right)$. The graph has a horizontal asymptote at $y=-1$. The graph crosses the $x$-axis at $x=-1$ and $x=1$, and the $y$-axis at $y=2$.

On the following set of axes, sketch the graph of $y={\left[f\left(x\right)\right]}^2+1$, clearly showing any asymptotes with their equations and the coordinates of any local maxima or minima.

Describe the transformation by which $f\left(x\right)$ is transformed to $g\left(x\right)$.

State the range of $g$.

Sketch the graphs of $y=f\left(x\right)$ and $y=g\left(x\right)$ on the same axes, clearly stating the points of intersection with any axes.

Find the coordinates of P.

Showing any $x$ and $y$ intercepts, any maximum or minimum points and any asymptotes, sketch the following curves on separate axes.

$y=f(x)$;