This week in Precalc 11 we were learning what an absolute value and what a reciprocal function looks like.
Both have similarities but also many differences.
Both an absolute value graph and reciprocal function graph can either be linear or quadratic.
An absolute value graph looks either like a V or W if quadratic and the graph is never in quadrants 3 or 4 due to the fact it is an absolute value meaning there can be no negatives. Critical points are the X-intercepts and where the graph starts to reflect. Below are the different types of what an absolute value graph may look like.
Linear:
Quadratic:
While a reciprocal function has two invariant points. and one vertical asymptote. An asymptote is an invisible barrier that separates the two values apart. Both a linear and quadratic reciprocal function graph hyperbolas are created which follow the asymptotes before hitting the invariant points and then follow back to the asymptote. Below are the different types of what a reciprocal function graph can look like.
Linear:
Quadratic: