Скачать или смотреть [ Pre-Calculus/SAT/AP exam/IB exam ]-- (Quiz-)--Composite Function Simplification and Graphing

This Video (based on our math blog and class recordings) presents a detailed solution to a complex mathematical problem requiring the determination and sketching of a function, $k(x)$. The primary task involves simplifying the rational expression $k(x) = f(x) \cdot g(x) / f(x)$, where $\mathbf{f(x) = (x-3)^2 - 4}$ and $\mathbf{g(x) = \sqrt{x+6}}$. The explanation meticulously walks through the process of $\mathbf{simplifying}$ the function by canceling $f(x)$, which then necessitates $\mathbf{identifying}$ the values of $x$ that make $f(x)$ zero, resulting in $\mathbf{undefined}$ points at $x=1$ and $x=5$. Furthermore, the solution $\mathbf{determines}$ the domain of $k(x)$ by combining the restriction from $\mathbf{g(x)}$ (where $\mathbf{x \ge -6}$) with the two excluded points. Finally, the source $\mathbf{describes}$ how to sketch the graph, which looks like the square root function $\mathbf{\sqrt{x+6}}$ but features $\mathbf{two holes}$ at the excluded points, thus emphasizing the importance of checking for excluded values after algebraic simplification.



Copyright all rights reserved
Full video check Youtube @mathtutor8285