Log Graphs

Front

What is the general shape of a logarithmic graph?

Back

Logarithmic graphs are typically increasing and have a vertical asymptote along the y-axis.

Front

What does the base of a logarithm indicate in the graph of a logarithmic function?

Back

The base of a logarithm indicates the rate at which the function increases. A larger base results in a slower increase.

Front

How does the graph of y = log_b(x) behave as x approaches 0 from the right?

Back

As x approaches 0 from the right, y approaches negative infinity.

Front

What transformation occurs when you translate the graph of y = log_b(x) 6 units left?

Back

The new function will be y = log_b(x + 6), shifting the graph left.

Front

What is the effect of translating the graph of y = log_b(x) 4 units up?

Back

The new function will be y = log_b(x) + 4, shifting the graph up.

Front

What is the reflection of the graph y = ln(x) over the y-axis?

Back

The reflection over the y-axis gives the graph y = ln(-x).

Front

How do you identify the vertical asymptote of a logarithmic function?

Back

The vertical asymptote of a logarithmic function y = log_b(x) is at x = 0.

Front

What is the relationship between the logarithmic function and its inverse?

Back

The inverse of a logarithmic function is an exponential function.

Front

What does the notation log_b(x + c) represent in terms of graph transformation?

Back

It represents a horizontal shift of the graph to the left by c units.

Front

How does changing the base of a logarithm affect its graph?

Back

Changing the base alters the steepness of the graph; a larger base results in a flatter graph.