Find the Range y=1/3x

Problem

y=1/(3*x)

Solution

1. Identify the type of function. This is a rational function of the form y=k/x where k=1/3

2. Determine the horizontal asymptote. For a rational function where the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is y=0

3. Analyze the behavior of the function. As x approaches infinity or negative infinity, y approaches 0 but never actually reaches it.

4. Solve for x in terms of y to find possible values of y

x=1/(3*y)

5. Observe the restriction on the variable y Since y is in the denominator, y cannot be equal to 0

6. Conclude that the range consists of all real numbers except 0

Final Answer

Range: *{[y∈ℝ,y≠0]}

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