Logarithmic Transformations

What is the domain of the function y = log(x - 2)?

• x > 0

• x > 1

• x > 2

• x > 3

What is the equation of the asymptote for the function y = log(x + 3)?

• x = 0

• x = 3

• x = -3

• y = 0

If logₐ(b) = c, what is the equivalent exponential form?

• a^c = b

• c = a^b

• b = a^c

• logₐ(c) = b

What is the value of log₂(8)?

• 1

• 2

• 3

• 4

Classify the following graph: y = log(x)

• Linear

• Quadratic

• Logarithmic

• Exponential

Describe the graph of f(x) = log x changed to f(x) = 3log(x + 1) - 5

• vertical stretch by 3 and shift left 1 and 5 units down

• horizontal compression by 3 and shift right 1 and 5 units up

• vertical compression by 3 and shift left 1 and 5 units down

• no transformation applied

What is the base of the logarithm in log₄(16)?

• 2

• 4

• 8

• 16

What transformation occurs when you change y = log(x) to y = log(x) + 3?

• Vertical shift down by 3 units.

• Vertical shift up by 3 units.

• Horizontal shift to the right by 3 units.

• Horizontal shift to the left by 3 units.

If f(x) = log(x), what is f(10)?

• 0

• 1

• 2

• 10

The asymptote of y = log₂x + 1 will shift...

• shift to x = 1

• shift to x = -1

• not shift at all and remain x = 0

• shift to y = 1