To sketch: The graph of which satisfies the conditions, , f is even.
Recall the definition of horizontal asymptote, “The line is called a horizontal asymptote of the curve if or ”.
Recall the definition that the line is said to be a vertical asymptote of the function , if at least one of the following conditions must be true:, , and .
The means that means that is a vertical asymptote to the function f. That is, as x approaches 3, the graph of the curve approaches negative infinity.
The means that is a horizontal asymptote to the function f as x approaches infinity.
The graph must contain a point (0, 0) as . So, mark the point (0, 0) as a filled dot.
Here, the function f is even. That is, .
Since and f is even, write and .
Thus, the possible graph of is shown below in Figure 1.
Use the above information and obtain the graph of as shown below in Figure 1.
Thus, the required graph of f.
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