Questions: Sketch the graph of the rational function. y = 1 / (x + 9)

Transcript text: Sketch the graph of the rational function. \[ y=1 /(x+9) \]

Solution

Solution Steps

Step 1: Find the vertical asymptote.

The vertical asymptote occurs when the denominator is equal to zero.

x + 9 = 0 x = -9

Step 2: Find the horizontal asymptote.

Since the degree of the numerator (0) is less than the degree of the denominator (1), the horizontal asymptote is y = 0.

Step 3: Analyze the behavior of the function.

Since the numerator is positive and the denominator is x + 9, the function will be positive when x > -9 and negative when x < -9.

Final Answer:

The correct graph is the top left one, which shows a vertical asymptote at x = -9, a horizontal asymptote at y = 0, and the function being positive for x > -9 and negative for x < -9.

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Questions: Sketch the graph of the rational function. y = 1 / (x + 9)

Solution

Solution Steps

Final Answer:

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