Lesson Worksheet: Graphs of Logarithmic Functions Mathematics

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In this worksheet, we will practice sketching logarithmic functions with different bases and their transformations and studying their different characteristics.

Q1:

Which curve is 𝑦=(𝑥)log?

  • A(b)
  • B(d)
  • C(a)
  • D(c)

Q2:

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

  • A
  • B
  • C
  • D
  • E

Q3:

Which function represents the following graph?

  • A𝑓(𝑥)=(𝑥)log
  • B𝑓(𝑥)=(2𝑥)log
  • C𝑓(𝑥)=(2𝑥)log
  • D𝑓(𝑥)=(𝑥)log
  • E𝑓(𝑥)=(𝑥)log

Q4:

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

𝑥−212
ℎ(𝑥)⋯⋯⋯
  • Aundefined, 1,2
  • B0.25,2,1
  • C−1,2,4
  • Dundefined, 0, 1

Q5:

Fill in the blank: All the curves of logarithmic functions, 𝑓(𝑥)=𝑥log, for any positive base 𝑎≠1 pass through the point .

  • A(1,0)
  • B(𝑎,0)
  • C(0,𝑎)
  • D(1,𝑎)
  • E(0,1)

Q6:

Consider the function 𝑓(𝑥)=(−𝑥)log.

Which graph represents this function?

  • A
  • B
  • C
  • D
  • E

Which of the following is an approximated value of 𝑓(−0.2)?

  • A1.15
  • B−2.32
  • C2.32
  • D0.87
  • EUndefined

Q7:

If the graph of 𝑓(𝑥)=𝑥log passes through the point (ℎ,3), find the value of ℎ.

Q8:

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 log2≈0.30.

  • 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

Q9:

For which values of 𝑎 is the function 𝑓(𝑥)=𝑥log decreasing?

  • A𝑎∈(0,1]
  • B𝑎∈(0,1)
  • C𝑎∈[0,1]
  • D𝑎∈[0,1)

Q10:

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

  • A𝑏=𝑎+4
  • B𝑏=16𝑎
  • C𝑏=𝑎
  • D𝑏=4𝑎

This lesson includes 20 additional questions and 195 additional question variations for subscribers.

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