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 subject to the given conditions, we need to consider the following: 1. Horizontal asymptote: \( y=0 \) 2. Vertical asymptote: \( x=-1 \) 3. \( y \)-intercept: \( (0,1) \) 4. No \( x \)-intercepts 5. Range: \( (0, \infty) \) Given the horizontal asymptote \( y=0 \), the rational function will have a horizontal asymptote at \( y=0 \). The vertical asymptote at \( x=-1 \) indicates that the function will have a vertical asymptote at \( x=-1 \). The \( y \)-intercept at \( (0,1) \) means that the function will pass through the point \( (0,1) \). Since there are no \( x \)-intercepts, the function will not cross the x-axis. The range of the function is \( (0, \infty) \), which means the function will only take positive values. To sketch the rational function, we can start by plotting the vertical asymptote at \( x=-1 \) and the horizontal asymptote at \( y=0 \). Then, we can plot the \( y \)-intercept at \( (0,1) \) and ensure that the function does not cross the x-axis. Finally, we can sketch the function to satisfy the given conditions.