Question

which statements describe key features of function f?range of {y| 0 < y < ∞}y-intercept at (0, 1)horizontal asymptote of y = 0horizontal asymptote of y = 2x-intercept at (3, 0)domain of {x|-1 < x < ∞}

Explanation:

1. Range: The graph lies entirely above the x-axis (y>0) and extends upward infinitely, so the range is $\{y|0 < y < \infty\}$.
2. y-intercept: The graph crosses the y-axis at (0,1), so this is correct.
3. Horizontal Asymptote: The graph approaches the line $y=0$ (the x-axis) as x increases, so $y=0$ is the horizontal asymptote.
4. Incorrect options: The graph has no x-intercept (never crosses the x-axis), the horizontal asymptote is not $y=2$, and the domain includes all real numbers (not just $x>-1$), so these are wrong.

Answer:

• range of $\{y|0 < y < \infty\}$
• y-intercept at $(0, 1)$
• horizontal asymptote of $y = 0$