Transformations of Log Functions

Front

Condense: log(2) + 3log(x)

Back

log(2x^3)

Front

What transformation occurs in the function y = log(x + 3)?

Back

left 3

Front

What is the transformation for: -log10(x)?

Back

reflection across the x-axis

Front

What is the equation of the vertical asymptote for log(x + 5) - 1?

Back

x = -5

Front

Solve: 4^(x + 5) = 16

Back

-3

Front

What is the base of the logarithm in log(x)?

Back

10 (common logarithm) or e (natural logarithm) depending on context.

Front

What does the graph of y = log(x) look like?

Back

It passes through (1,0), approaches the y-axis (x=0) as a vertical asymptote.

Front

What is the effect of adding a constant to a logarithmic function, e.g., y = log(x) + 2?

Back

It shifts the graph up by 2 units.

Front

What is the effect of subtracting a constant from a logarithmic function, e.g., y = log(x) - 2?

Back

It shifts the graph down by 2 units.

Front

What happens to the graph of y = log(x) when x is replaced with (x - 3)?

Back

It shifts the graph to the right by 3 units.