Log Graph Transformations

Front

What is the transformation of the function f(x) = -log₂(x+1)?

Back

The function is transformed by shifting left one unit and reflecting across the x-axis.

Front

What is the domain of the function y = log₂(x+1)?

Back

The domain is (-1, ∞).

Front

What is the range of the function y = log₂(x+1)?

Back

The range is (-∞, ∞).

Front

Write the equation of the function f(x) = log₃(x) after translating 6 units left and 4 units up.

Back

g(x) = log₃(x + 6) + 4.

Front

Match the graph with its equation: y = log₆(x − 2) + 1.

Back

This equation represents a logarithmic function shifted right by 2 units and up by 1 unit.

Front

What does a reflection across the y-axis do to the function f(x) = log₂(x)?

Back

It transforms the function to f(x) = log₂(-x), which reflects the graph over the y-axis.

Front

How does the graph of y = log₃(x) change when it is translated 3 units to the right?

Back

The new function is y = log₃(x - 3), shifting the graph right.

Front

What is the effect of a vertical stretch on the function f(x) = log₂(x)?

Back

A vertical stretch by a factor of a results in g(x) = a * log₂(x), making the graph steeper.

Front

What is the vertical asymptote of the function y = log₂(x + 1)?

Back

The vertical asymptote is at x = -1.

Front

Describe the transformation of the function f(x) = log₆(x) when it is reflected across the x-axis.

Back

The transformed function is f(x) = -log₆(x), which flips the graph over the x-axis.