Worksheet: Graphs of Logarithmic Functions

In this lesson, we will learn how to sketch logarithmic functions with different bases and their transformations and we will study their 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?

  • A𝑎(0,1]
  • B𝑎(0,1)
  • C𝑎[0,1]
  • D𝑎[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(1.44,0.36), (0.72,0.33)
  • B(0.36,1.03), (1.83,0.60)
  • C(0.36,1.03), (1.83,0.60)
  • D(1.03,0.36), (0.60,1.83)
  • E(0.36,1.44), (0.33,0.72)

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:

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

Q6:

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

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

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

Q9:

Which of the following functions is increasing?

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

Q10:

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

  • AIncreasing
  • BUndefined
  • CDecreasing

Q11:

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

𝑥212
(𝑥)
  • Aundefined, 1,2
  • B0.25,2,1
  • C1,2,4
  • Dundefined, 0, 1

Q12:

Determine the point at which the graph of the function 𝑓(𝑥)=(18𝑥)log intersects the 𝑥-axis.

  • A(17,0)
  • B(0,15)
  • C(0,17)
  • D(15,0)
  • E(0,34)

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