Question

Sketch the graph of the function fwhere the domain is \(\left( { - {\bf{2}},{\bf{2}}} \right)\),\(f'\left( {\bf{0}} \right) = - {\bf{2}}\), \(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{2}}^ - }} f\left( x \right) = \infty \), f is continuous at all numbers in its domain except \( \pm {\bf{1}}\), and f is odd.

Short answer

The sketch of the graph of the function is shown below:

Step-by-step solution

Step 1:Write an interpretation of given information for g

Following observations can be made about the function \(g\left( x \right)\).

1. Since f is odd, f is symmetric in the opposite quadrant.
2. The equation \(f'\left( 0 \right) = - 2\)shows that the slope of the tangent at \(x = 0\) is \( - 2\).
3. The equation \(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \infty \) shows that as x is approaching 2 from the right, \(f\left( x \right)\) will approach to \(\infty \).

Sketch the graph of the function

The figure below represents the graph of \(f\left( x \right)\).

Thus, the sketch of the curve function is obtained.