Function Graphs C80176

1. **State the problem:** We are given two functions: $$f(x) = \frac{3}{x-2}$$ and $$g(x) = \sqrt{x+1}$$. We want to understand their shapes and graph characteristics. 2. **Analyze $f(x)$:** This is a rational function with a vertical asymptote at $x=2$ because the denominator becomes zero there. 3. **Analyze $g(x)$:** This is a square root function shifted left by 1 unit. The domain is $x \geq -1$ because the expression inside the square root must be non-negative. 4. **Graph shape for $g(x)$:** The graph starts at the point $(-1,0)$ and increases to the right, forming the classic square root curve shape. 5. **Summary:** $f(x)$ has a hyperbola shape with a vertical asymptote at $x=2$. $g(x)$ is a square root curve starting at $x=-1$ and increasing to the right. **Final answer:** The graph of $g(x)$ is a square-root curve starting at $x=-1$ and increasing to the right, positioned top-right relative to $f(x)$'s vertical asymptote at $x=2$.