Sketch a rational function subject to the given conditions. Horizontal asymptote: \( y=0 \) Vertical asymptote: \( x=-1 \) \( y \)-intercept: \( (0,1) \) No \( x \)-intercepts Range: \( (0, \infty) \)

To sketch a rational function that meets your criteria, consider the function \( f(x) = \frac{1}{x + 1} \). 1. The horizontal asymptote is \( y=0 \) since as \( x \) approaches infinity, \( f(x) \) approaches 0. 2. The vertical asymptote at \( x=-1 \) occurs because the function is undefined there, causing it to diverge to infinity or negative infinity on either side. 3. The \( y \)-intercept is \( (0, 1) \) since \( f(0) = 1 \). 4. The function has no \( x \)-intercepts; it never crosses the x-axis because the output is always positive for all values of \( x \) in the domain, and it only approaches the x-axis as \( x \) goes to positive or negative infinity. 5. The range is \( (0, \infty) \) as the function only produces positive outputs. Thus, our rational function is well-suited to your requirements! Grab your markers and start sketching this delightful curve!