Worksheet: Graphs of Logarithmic Functions

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In this worksheet, we will practice sketching logarithmic functions and determining the function behavior at infinity.

Q1:

Which curve is 𝑦 = ( 𝑥 ) l o g 3 ?

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q2:

For which values of 𝑎 is the function 𝑓 ( 𝑥 ) = 𝑥 l o g decreasing?

  • A 𝑎 ∈ [ 0 , 1 [
  • B 𝑎 ∈ [ 0 , 1 ]
  • C 𝑎 ∈ ] 0 , 1 ]
  • D 𝑎 ∈ ] 0 , 1 [

Q3:

Use technology to plot the graphs of 𝑓 ( 𝑥 ) = 𝑥 − 3 𝑥 3 and 𝑔 ( 𝑥 ) = 𝑥 l n . Find the coordinates where 𝑓 ( 𝑥 ) = 𝑔 ( 𝑥 ) if the curves intersect, giving your answer to two decimal places.

  • A ( 1 . 4 4 , 0 . 3 6 ) , ( 0 . 7 2 , 0 . 3 3 )
  • B ( 0 . 3 6 , 1 . 0 3 ) , ( 1 . 8 3 , − 0 . 6 0 )
  • C ( 0 . 3 6 , 1 . 4 4 ) , ( 0 . 3 3 , 0 . 7 2 )
  • D ( 0 . 3 6 , − 1 . 0 3 ) , ( 1 . 8 3 , 0 . 6 0 )
  • E ( 1 . 0 3 , 0 . 3 6 ) , ( 0 . 6 0 , 1 . 8 3 )

Q4:

Use the graph of 𝑦 = 1 0 𝑥 to list the values of l o g 𝑛 for 𝑛 = 2 , … , 6 to two decimal places. For example, we see that l o g 2 ≈ 0 . 3 0 .

  • A 0.30, 0.35, 0.60, 0.70, 0.75
  • B 0.18, 0.30, 0.40, 0.477, 0.544
  • C 0.20, 0.30, 0.60, 0.70, 0.78
  • D 0.30, 0.48, 0.60, 0.70, 0.78
  • E 0.30, 0.40, 0.60, 0.80, 0.90

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