Worksheet: Graphs of Logarithmic Functions

In this worksheet, we will practice sketching the logarithmic function and its transformation and studying its different characteristics.

Q1:

Which curve is 𝑦=(𝑥)log?

  • A(b)
  • B(d)
  • C(a)
  • D(c)

Q2:

For which values of 𝑎 is the function 𝑓(𝑥)=𝑥log 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)=𝑥3𝑥 and 𝑔(𝑥)=𝑥ln. 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 . 0 3 ) , ( 1 . 8 3 , 0 . 6 0 )
  • D ( 1 . 0 3 , 0 . 3 6 ) , ( 0 . 6 0 , 1 . 8 3 )
  • E ( 0 . 3 6 , 1 . 4 4 ) , ( 0 . 3 3 , 0 . 7 2 )

Q4:

Use the graph of 𝑦=10 to list the values of log𝑛 for 𝑛=2,,6 to two decimal places. For example, we see that log20.30.

  • A0.20, 0.30, 0.60, 0.70, 0.78
  • B0.30, 0.35, 0.60, 0.70, 0.75
  • C0.30, 0.40, 0.60, 0.80, 0.90
  • D0.18, 0.30, 0.40, 0.477, 0.544
  • E0.30, 0.48, 0.60, 0.70, 0.78

Q5:

Find the missing table values for (𝑥)=𝑥log.

𝑥 2 1 2
( 𝑥 )
  • Aundefined, 1,2
  • B 0 . 2 5 , 2 , 1
  • C 1 , 2 , 4
  • Dundefined, 0, 1

Q6:

Given that the figure shows the graph of the function 𝑓(𝑥)=𝑥log, express 𝑏 in terms of 𝑎.

  • A 𝑏 = 𝑎 + 4
  • B 𝑏 = 1 6 𝑎
  • C 𝑏 = 𝑎
  • D 𝑏 = 4 𝑎

Q7:

The graph of the function 𝑓𝑓(𝑥)=𝑥log passes through the point (512,𝑘). What is the value of 𝑘?

Q8:

Which graph represents the function 𝑓(𝑥)=(𝑥)log?

  • A
  • B
  • C
  • D
  • E

Q9:

Which function represents the following graph?

  • A 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • B 𝑓 ( 𝑥 ) = ( 2 𝑥 ) l o g
  • C 𝑓 ( 𝑥 ) = ( 2 𝑥 ) l o g
  • D 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • E 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g

Q10:

Which of the following functions is increasing?

  • A 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • B 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • C 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • D 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g
  • E 𝑓 ( 𝑥 ) = ( 𝑥 ) l o g

Q11:

Specify the behavior of the function 𝑓(𝑥)=(𝑥)log.

  • AIncreasing
  • BUndefined
  • CDecreasing

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