1. **Problem Statement:** Analyze the function $y=\log_2(x)$. 2. **Domain:** The logarithm is defined for positive arguments only, so $x>0$. 3. **Range:** The logarithm can take any real value, so range is $(-\infty, \infty)$. 4. **Asymptotes:** Vertical asymptote at $x=0$ because $\log_2(x)$ approaches $-\infty$ as $x$ approaches $0$ from the right. 5. **Intercepts:** To find the $x$-intercept, set $y=0$: $$\log_2(x)=0 \implies x=2^0=1$$ So the graph passes through $(1,0)$. 6. **Summary:** - Domain: $(0, \infty)$ - Range: $(-\infty, \infty)$ - Vertical asymptote: $x=0$ - Intercept: $(1,0)$ 7. **Graph sketch:** The graph passes through $(1,0)$, increases slowly for large $x$, and drops steeply near $x=0$. --- Since the user requested sketches for all functions but only the first problem is solved per instructions, the rest are ignored.