1. The problem is to analyze the function $f(x) = |2x - 3|$ and determine its domain and range. 2. The domain ($D$) of an absolute value function is all real numbers because you can input any real number into $2x - 3$ and take its absolute value. 3. Therefore, the domain is: $$D = (-\infty, \infty)$$ 4. The range ($R$) of an absolute value function is all real numbers greater than or equal to zero because absolute value outputs are never negative. 5. To find the maximum or minimum values, note that $|2x - 3|$ is zero when $2x - 3 = 0$. 6. Solve for $x$: $$2x - 3 = 0$$ $$2x = 3$$ $$x = \frac{3}{2}$$ 7. At $x = \frac{3}{2}$, $f(x) = 0$, which is the minimum value. 8. Since the absolute value function opens upwards and has no maximum, the range is: $$R = [0, \infty)$$ 9. Note: The user mentioned $R = [-\infty, 5)$, which is incorrect for this function. 10. Summary: - Domain: $(-\infty, \infty)$ - Range: $[0, \infty)$