Exp & Log Graphs

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to obtain a given number.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to produce a given number. Common bases are 10 (common logarithm) and e (natural logarithm).

Front

What is the vertical asymptote of a logarithmic function?

Back

The vertical asymptote of a logarithmic function is the line x = 0.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is typically y = 0.

Front

How does the graph of y = log(x) behave as x approaches 0?

Back

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

Front

What transformation does y = log(x + 4) represent?

Back

The graph of y = log(x + 4) is shifted 4 units to the left compared to y = log(x).

Front

What transformation does y = log(x) - 4 represent?

Back

The graph of y = log(x) - 4 is shifted 4 units down compared to y = log(x).

Front

What is the transformation of the function f(x) = 2^{x+5} - 7?

Back

The graph is shifted 5 units to the left and 7 units down.

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

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

Back

The domain of y = log(x) is x > 0.