# 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 ? • A(b)
• B(d)
• C(a)
• D(c)

Q2:

For which values of is the function decreasing?

• A
• B
• C
• D

Q3:

Use technology to plot the graphs of and . Find the coordinates where if the curves intersect, giving your answer to two decimal places.

• A,
• B,
• C,
• D,
• E,

Q4:

Use the graph of to list the values of for to two decimal places. For example, we see that . • 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 , express in terms of . • A
• B
• C
• D

Q6:

The graph of the function passes through the point . What is the value of ?

Q7:

Which graph represents the function ?

• A • B • C • D • E Q8:

Which function represents the following graph? • A
• B
• C
• D
• E

Q9:

Which of the following functions is increasing?

• A
• B
• C
• D
• E

Q10:

Specify the behavior of the function .

• AIncreasing
• BUndefined
• CDecreasing

Q11:

Find the missing table values for .

 𝑥 ℎ(𝑥) −2 1 2
• Aundefined,
• B
• C
• Dundefined, 0, 1

Q12:

Determine the point at which the graph of the function intersects the -axis.

• A
• B
• C
• D
• E