Log Graph Transformations

Front

What is the general form of a logarithmic function?

Back

f(x) = log_b(x) where b > 0 and b ≠ 1.

Front

What does it mean to translate a function 6 units left?

Back

Replace x with (x + 6) in the function.

Front

What does it mean to translate a function 4 units up?

Back

Add 4 to the entire function.

Front

What is the asymptote of the function y = log_b(x)?

Back

The vertical asymptote is x = 0.

Front

How do you find the range of a logarithmic function?

Back

The range of y = log_b(x) is (-∞, ∞).

Front

What is the effect of adding a constant to a logarithmic function?

Back

It translates the graph vertically.

Front

What is the effect of subtracting a constant from a logarithmic function?

Back

It also translates the graph vertically.

Front

What is the effect of multiplying the input of a logarithmic function by a constant?

Back

It compresses or stretches the graph horizontally.

Front

What is the effect of multiplying the logarithmic function by a constant?

Back

It stretches or compresses the graph vertically.

Front

Write the equation of the function f(x) = log_3(x) after translating 6 units left and 4 units up.

Back

g(x) = log_3(x + 6) + 4.