# Worksheet: Graphs of Logarithmic Functions

In this worksheet, we will practice sketching the logarithmic function and its transformation and studying its 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:

Find the missing table values for .

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

Q6:

Given that the figure shows the graph of the function , express in terms of .

• A
• B
• C
• D

Q7:

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

Q8:

Which graph represents the function ?

• A
• B
• C
• D
• E

Q9:

Which function represents the following graph?

• A
• B
• C
• D
• E

Q10:

Which of the following functions is increasing?

• A
• B
• C
• D
• E

Q11:

Specify the behavior of the function .

• AIncreasing
• BUndefined
• CDecreasing