1. **State the problem:** Find the features of the graph of the function $$f(x) = \frac{4}{2x + 3}$$ including horizontal and vertical asymptotes, intercepts, and holes. 2. **Horizontal asymptote:** For rational functions, if the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is $$y = 0$$. 3. **Vertical asymptote:** Set the denominator equal to zero and solve for $$x$$: $$2x + 3 = 0$$ $$2x = -3$$ $$x = \frac{-3}{2}$$ So, the vertical asymptote is $$x = -\frac{3}{2}$$. 4. **x-intercept:** Set the numerator equal to zero and solve for $$x$$: $$4 = 0$$ This is never true, so there is no x-intercept. 5. **y-intercept:** Evaluate $$f(0)$$: $$f(0) = \frac{4}{2(0) + 3} = \frac{4}{3}$$ So, the y-intercept is $$\left(0, \frac{4}{3}\right)$$. 6. **Hole:** Holes occur where numerator and denominator share a common factor. Here, numerator is 4 (constant) and denominator is $$2x + 3$$, so no common factors and no holes. **Final answers:** - Horizontal asymptote: $$y = 0$$ - Vertical asymptote: $$x = -\frac{3}{2}$$ - x-intercept: None - y-intercept: $$\left(0, \frac{4}{3}\right)$$ - Hole: None