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Lesson: Reciprocal Function Characteristics

Sample Question Videos

Worksheet • 3 Questions • 1 Video

Q1:

The figure shows the graph of 𝑦 = 1 π‘₯ .

Write down the equations of the two asymptotes of 𝑦 = 1 π‘₯ .

  • A 𝑦 = 0 and π‘₯ = 0
  • B 𝑦 = 1 and π‘₯ = 0
  • C 𝑦 = 0 and π‘₯ = 1
  • D 𝑦 = 1 and π‘₯ = 1
  • E 𝑦 = βˆ’ 1 and π‘₯ = βˆ’ 1

What is the domain of the function?

  • A π‘₯ ∈ ℝ , π‘₯ β‰  0
  • B π‘₯ ∈ ( βˆ’ ∞ , 0 )
  • C π‘₯ ∈ ℝ
  • D π‘₯ ∈ ( 1 , ∞ )
  • E π‘₯ ∈ ( 0 , ∞ )

What is the range of the function?

  • A 𝑦 ∈ ℝ , 𝑦 β‰  0
  • B 𝑦 ∈ ( βˆ’ ∞ , 0 )
  • C 𝑦 ∈ ℝ
  • D 𝑦 ∈ ( 1 , ∞ )
  • E 𝑦 ∈ ( 0 , ∞ )

Q2:

The following is the graph of the triangle wave function 𝑦 = 𝑔 ( π‘₯ ) .

What is the domain of its reciprocal function 𝑓 ( π‘₯ ) = 1 𝑔 ( π‘₯ ) ?

  • Aall real numbers that are not integers
  • Ball integers
  • Call real numbers
  • Dodd integers
  • Eeven integers

Q3:

Consider the function 𝑦 = 3 π‘₯ 5 π‘₯ + 7 .

By considering the point at which the denominator equals zero, find the domain of the function.

  • A π‘₯ ∈ ℝ , π‘₯ β‰  βˆ’ 7 5
  • B π‘₯ ∈ ℝ , π‘₯ β‰  3 5
  • C π‘₯ ∈ ℝ , π‘₯ β‰  7 5
  • D π‘₯ ∈ ℝ , π‘₯ β‰  5 7
  • E π‘₯ ∈ ℝ , π‘₯ β‰  βˆ’ 5 7

To find the range of the function, a handy trick is to divide the numerator and denominator of 3 π‘₯ π‘₯ + 7 through by π‘₯ . What expression does this give us?

  • A 3 5 +  
  • B 3 5 π‘₯ + 7
  • C 3 5 + 7
  • D 3 π‘₯ 5 +  

Now, taking the limit of this expression as π‘₯ tends to infinity will give us the value of 𝑦 which is not in the range of the original function. Use this to state the range of the function.

  • A 𝑦 ∈ ℝ , 𝑦 β‰  3 5
  • B 𝑦 ∈ ℝ , 𝑦 β‰  βˆ’ 3 7
  • C 𝑦 ∈ ℝ , 𝑦 β‰  3 7
  • D 𝑦 ∈ ℝ , 𝑦 β‰  βˆ’ 3 5
  • E 𝑦 ∈ ℝ , 𝑦 β‰  1 4

Hence, state the equations of the two asymptotes.

  • A 𝑦 = 3 5 and π‘₯ = βˆ’ 7 5
  • B 𝑦 = 3 7 and π‘₯ = 7 5
  • C 𝑦 = 3 5 and π‘₯ = 7 5
  • D 𝑦 = 1 4 and π‘₯ = 3 5
  • E 𝑦 = 3 7 and π‘₯ = βˆ’ 7 5
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