Use the curve-sketching guideline, to sketch the graph of the function.
A)
B)
C)

Question

Use the curve-sketching guideline, to sketch the graph of the function. ​  ​
A) ​ 
B) ​ 
C) ​

Quizplus · Accepted Answer

1. Domain: The function is defined for all real numbers.
2. Intercepts: 
Y-intercept: (0, 1)
X-intercept: No real x-intercepts.
3. Symmetry: The function is an odd function, which means it is symmetric about the origin.
4. Asymptotes: There are no vertical asymptotes. The horizontal asymptote is y = 0, since as x approaches infinity or negative infinity, the function approaches 0.
5. Intervals of Increase and Decrease: The function is decreasing on the interval (-infinity, 0) and increasing on the interval (0, infinity).
6. Local Maxima and Minima: No local maxima or minima.
7. Concavity: The function is concave down on the interval (-infinity, -sqrt(2)] and concave up on the interval [-sqrt(2), sqrt(2)] and concave down on the interval [sqrt(2), infinity).
8. Inflection Points: The function has one inflection point at (-sqrt(2), 0) and (sqrt(2), 0).
9. Sketch the graph of the function using the above information.

Use the Curve-Sketching Guideline, to Sketch the Graph of the Function