Using the curve-sketching guide, select the graph of the function.

Question

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1. Domain: The function is defined for all real numbers.
2. Intercepts: The y-intercept is approximately (0, 2). There are no x-intercepts.
3. Symmetry: The function is neither even nor odd.
4. Asymptotes: There is a horizontal asymptote at y = 1 and a vertical asymptote at x = 2.
5. Intervals of Increase/Decrease: The function decreases on (-∞,2) and increases on (2,∞).
6. Local Extrema: There is a relative minimum at (0, 2).
7. Concavity: The function is concave up on (2,∞) and concave down on (-∞,2).
8. Points of Inflection: There is a point of inflection at approximately (1.3, 1.5).
9. Sketch the Graph: Combining all of the above information, we can sketch the graph of the function. Only option B matches all of the above conditions.

Using the Curve-Sketching Guide, Select the Graph of the Function