Practice: Graphs of Rational Functions

Consider the graph of the function 𝑦=1𝑥.

By looking at the graph and substituting a few successively larger values of 𝑥 into the function, what is the end behavior of the graph as 𝑥 increases along the positive 𝑥-axis?

  • AThe value of 𝑦 approaches infinity as 𝑥 increases.
  • BThe value of 𝑦 approaches negative infinity as 𝑥 increases.
  • CThe value of 𝑦 approaches zero as the value of 𝑥 increases.

Similarly, what is the end behavior of the graph as 𝑥 decreases?

  • AThe value of 𝑦 approaches zero.
  • BThe value of 𝑦 approaches .
  • CThe value of 𝑦 approaches .

Finally, by interpreting the graph, what is happening to the function when the value of 𝑥 approaches zero?

  • AThe value of 𝑦 approaches negative infinity when 𝑥 gets closer to zero from the negative direction or from the positive direction.
  • BThe value of 𝑦 approaches negative infinity when 𝑥 gets closer to zero from the negative direction and approaches positive infinity when 𝑥 gets closer to zero from the positive direction.
  • CThe value of 𝑦 approaches positive infinity when 𝑥 gets closer to zero from the negative direction and approaches negative infinity when 𝑥 gets closer to zero from the positive direction.
  • DThe value of 𝑦 approaches positive infinity when 𝑥 gets closer to zero from the negative direction or from the positive direction.

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