1. **State the problem:** Solve the equation $$y = |\log_2\left(3 - \frac{1}{2}x\right)| + 5$$ and understand its behavior. 2. **Recall the logarithm domain rule:** The argument of the logarithm must be positive, so $$3 - \frac{1}{2}x > 0$$ which implies $$\frac{1}{2}x < 3 \implies x < 6$$. 3. **Rewrite the function inside the absolute value:** $$y = \left| \log_2\left(3 - \frac{1}{2}x\right) \right| + 5$$ 4. **Analyze the logarithm:** - The logarithm base 2 means we are looking for the power to which 2 must be raised to get the argument. - The absolute value means the output of the logarithm is always non-negative. 5. **Find intercepts:** - To find the y-intercept, set $$x=0$$: $$y = |\log_2(3 - 0)| + 5 = |\log_2(3)| + 5$$ Calculate $$\log_2(3) \approx 1.585$$, so $$y \approx 1.585 + 5 = 6.585$$. 6. **Domain and range:** - Domain: $$x < 6$$ - Range: Since absolute value is always $$\geq 0$$, and we add 5, range is $$[5, \infty)$$. 7. **Graph features:** - The function has a vertical asymptote as $$x \to 6^-$$ because the argument of the log approaches zero. - The function is always $$\geq 5$$. **Final answer:** The function $$y = |\log_2(3 - \frac{1}{2}x)| + 5$$ is defined for $$x < 6$$ with range $$[5, \infty)$$ and y-intercept approximately 6.585.