Practice: Intro to Log Functions

Front

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

Back

The domain of log(x) is (0, ∞). This means that log(x) is defined for all positive values of x.

Front

What is the range of the logarithmic function log(x)?

Back

The range of log(x) is (-∞, ∞). This means that log(x) can take any real number value.

Front

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

Back

The vertical asymptote of y = log(x) is x = 0. The graph approaches this line but never touches it.

Front

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

Back

The function y = log(x) does not have a horizontal asymptote.

Front

What is the general form of a logarithmic function?

Back

The general form of a logarithmic function is y = log_b(x - h) + k, where b is the base, (h, k) is the translation of the graph.

Front

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

Back

Changing the base of a logarithm affects the steepness of the graph. A larger base results in a flatter graph.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions. If y = log_b(x), then b^y = x.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1, because b^1 = b.