📘 advanced functions

1. **State the problem:** We are given three functions:

1. **Problem Statement:** Given functions $f(x) = x + 2$ and $g(x) = \frac{1}{x-9}$, find and analyze the composite function $h(x) = f(g(x))$. 2. **Find the equation of $h(x)$:**

1. **State the problem:** We need to analyze and sketch the graph of the function $$y = -2 \cos\left(0.25x - \frac{\pi}{8}\right) + 3$$ by finding its amplitude, axis of the curve,

1. **State the problem:** We want to determine if the bacteria count for the tap water sample, modeled by $$f(t) = \frac{5t}{t^2 + 3t + 2}$$, will ever exceed the bacteria count fo

1. **State the problem:** Solve the equation $$15\cot^3\left(3\left(\theta - \frac{\pi}{4}\right)\right) - \cot^2\left(3\left(\theta - \frac{\pi}{4}\right)\right) - 2\cot\left(3\le

1. Let's start with polynomial functions. 2. Polynomial inequalities involve finding where a polynomial is greater than or less than zero.