IB Mathematics Analysis and Approaches Question Type 3: Graphing Equations with the Absolute Values on the x Only Exercises

Sketch the graph of $$y=\frac{1}{|x|+1}$$ and state its horizontal asymptote and domain.

Sketch the graph of $y=|x{|}^3-2|x|$ and identify any local minima or maxima.

Sketch the graph of $y=2|x|+3$.

Sketch the graph of $y=|x{|}^2$ and describe its shape, domain, and range.

Sketch the graph of $y=|x{|}^2+4|x|+3$ and factorise to find its zeros.

Sketch the graph of $$y=e^{-|x|}$$ and state its $y$-intercept and end behavior as $x\to \pm \infty$.

Sketch the graph of $y=\sqrt{|x|}$.

Sketch the graph of $y=|x|$.

Sketch the graph of $y=|x|-5$ and determine its $x$- and $y$-intercepts.

Sketch the graph of $y=|x{|}^2-5|x|-6$ and find its $x$-intercepts.

Sketch the graph of $y=-|x|+4$.

Sketch the graph of $y=-2|x{|}^2+8$ and determine its vertex and intercepts.