Oblique Asymptote – can use simplified form of equation (factored).
Then sketch the graph!
Graphing Rational Functions
Graph using your information.
Points: (0,0), (3,0); POD @ x=-3; VA @ x=-1; OA @ y=x-4
Graphing Absolute Value Functions
If the function is linear, we can evaluate these as transformations that have been applied to y = |x|.
Ex: Sketch the graph of y = -2|x-5|
What transformations are there?
Horizontal translation +5
Stretch of 2
Reflection across the x-axis
If the function is non-linear – then simply graph the original and ‘flip’ the negative parts (like we did in class).
When simplifying a rational expression that is being multiplied or divided, factor first, simplify, then multiply top with top, bottom with bottom & state restrictions: no zeros in the denominator!
Ex: Simplify the following expression, stating any restrictions.
When simplifying a rational expression that is being added or subtracted, you need each expression to have the same denominator.
Ex. Solve for b.
When solving inequalities – remember the goal is to either isolate x, or set one side to zero. Simplify as much as you can. Either draw a graph or use the number line method – show your work, including test value(s).