Question

Sketch the graph of an example of a function\(f\)that satisfies all of the given conditions.

15. \(\mathop {lim}\limits_{x \to {1^ - }} f\left( x \right) = {\bf{3}}\), \(\mathop {lim}\limits_{x \to {1^ + }} f\left( x \right) = {\bf{0}}\), \(f\left( {\bf{1}} \right) = {\bf{2}}\).

Short answer

According to the given conditions, the value of the function \(f\left( x \right)\) approaches to \(3\) as \(x\) approaches to \(1\) from the left.

The value of function \(f\left( x \right)\) approaches to \(0\) as \(x\) approaches to \(1\) from the right. At \(x = 1\), the value of the function is \(2\).

Step-by-step solution

Observe the given conditions

According to the given conditions, the value of the function \(f\left( x \right)\) approaches to \(3\) as \(x\) approaches to \(1\) from the left.

The value of function \(f\left( x \right)\) approaches to \(0\) as \(x\) approaches to \(1\) from the right. At \(x = 1\), the value of the function is \(2\).

Plot the graph of the function

Use the information from step 1 and plot the graph as shown below:

Thus, the sketch of the graph is obtained.