1. **Problem statement:** We are given the function $b(x) = \frac{3}{3x - 4}$ defined on the interval $\left[\frac{4}{3}, +\infty\right[$. We want to understand its behavior and graph. 2. **Formula and domain:** The function is a rational function with denominator $3x - 4$. The domain excludes values where the denominator is zero, i.e., $3x - 4 \neq 0 \Rightarrow x \neq \frac{4}{3}$. Since the domain is $\left[\frac{4}{3}, +\infty\right[$, the function is defined starting exactly at $x = \frac{4}{3}$ but not at values less than that. 3. **Behavior near the boundary:** At $x = \frac{4}{3}$, the denominator is zero, so the function tends to infinity or negative infinity. We check the limit from the right: $$\lim_{x \to \frac{4}{3}^+} b(x) = \lim_{x \to \frac{4}{3}^+} \frac{3}{3x - 4} = +\infty$$ 4. **Asymptotic behavior:** For large $x$, the denominator $3x - 4 \approx 3x$, so $$b(x) \approx \frac{3}{3x} = \frac{1}{x}$$ which tends to 0 as $x \to +\infty$. 5. **Monotonicity:** The derivative is $$b'(x) = \frac{d}{dx} \left( \frac{3}{3x - 4} \right) = -\frac{9}{(3x - 4)^2}$$ Since the denominator squared is positive, $b'(x) < 0$ for all $x > \frac{4}{3}$, so $b(x)$ is strictly decreasing on its domain. 6. **Summary:** The function $b(x) = \frac{3}{3x - 4}$ is defined for $x \geq \frac{4}{3}$, tends to $+\infty$ as $x$ approaches $\frac{4}{3}$ from the right, decreases strictly, and tends to 0 as $x$ goes to infinity. **Final answer:** The graph is a strictly decreasing curve starting at $+\infty$ at $x=\frac{4}{3}$ and approaching 0 as $x \to +\infty$.