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

Start Practising

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, which of the following correctly expresses 𝑏 in terms of 𝑎.

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

Practice Means Progress

Download the Nagwa Practice app to access 25 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.