Lesson Worksheet: Graphs of Logarithmic Functions Mathematics • 10th Grade

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

Q1:

Which curve is ๐‘ฆ=(๐‘ฅ)log๏Šฉ?

  • A(b)
  • B(d)
  • C(a)
  • D(c)

Q2:

Which graph represents the function ๐‘“(๐‘ฅ)=(๐‘ฅ)log๏Šซ?

  • A
  • B
  • C
  • D
  • E

Q3:

Which function represents the following graph?

  • A๐‘“(๐‘ฅ)=(๐‘ฅ)log๏Šฎ
  • B๐‘“(๐‘ฅ)=(2๐‘ฅ)log๏Šจ
  • C๐‘“(๐‘ฅ)=(2๐‘ฅ)log๏Šช
  • D๐‘“(๐‘ฅ)=(๐‘ฅ)log๏Šจ
  • E๐‘“(๐‘ฅ)=(๐‘ฅ)log๏Šช

Q4:

Find the missing table values for โ„Ž(๐‘ฅ)=๐‘ฅlog๏Šจ.

๐‘ฅโˆ’212
โ„Ž(๐‘ฅ)โ‹ฏโ‹ฏโ‹ฏ
  • Aundefined, 1,2
  • B0.25,2,1
  • Cโˆ’1,2,4
  • Dundefined, 0, 1

Q5:

Fill in the blank: All the curves of logarithmic functions, ๐‘“(๐‘ฅ)=๐‘ฅlog๏Œบ, for any positive base ๐‘Žโ‰ 1 pass through the point .

  • A(1,0)
  • B(๐‘Ž,0)
  • C(0,๐‘Ž)
  • D(1,๐‘Ž)
  • E(0,1)

Q6:

Consider the function ๐‘“(๐‘ฅ)=(โˆ’๐‘ฅ)log๏Šจ.

Which graph represents this function?

  • A
  • B
  • C
  • D
  • E

Which of the following is an approximated value of ๐‘“(โˆ’0.2)?

  • A1.15
  • Bโˆ’2.32
  • C2.32
  • D0.87
  • EUndefined

Q7:

If the graph of ๐‘“(๐‘ฅ)=๐‘ฅlog๏Šจ passes through the point (โ„Ž,3), find the value of โ„Ž.

Q8:

Use the graph of ๐‘ฆ=10๏— to list the values of log๐‘› for ๐‘›=2,โ€ฆ,6 to two decimal places. For example, we see that log2โ‰ˆ0.30.

  • 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 ๐‘Ž is the function ๐‘“(๐‘ฅ)=๐‘ฅlog๏Œบ decreasing?

  • A๐‘Žโˆˆ(0,1]
  • B๐‘Žโˆˆ(0,1)
  • C๐‘Žโˆˆ[0,1]
  • D๐‘Žโˆˆ[0,1)

Q10:

Given that the figure shows the graph of the function ๐‘“(๐‘ฅ)=๐‘ฅlog๏Šจ, which of the following correctly expresses ๐‘ in terms of ๐‘Ž.

  • A๐‘=๐‘Ž+4
  • B๐‘=16๐‘Ž
  • C๐‘=๐‘Ž๏Šช
  • D๐‘=4๐‘Ž

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