Unit 4 Test Review #2: Graphing logarithms

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

What does the base of a logarithm indicate?

Back

The base of a logarithm indicates the number that is raised to a power to obtain a given value. For example, log_b(a) = c means b^c = a.

Front

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

Back

The domain of y = log_b(x) is (0, ∞), meaning x must be greater than 0.

Front

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

Back

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

Front

How does the graph of y = log_b(x) change when k is added?

Back

Adding k to the function, y = log_b(x) + k, shifts the graph vertically by k units.

Front

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

Back

The range of y = log_b(x) is (-∞, ∞), meaning it can take any real number value.

Front

What effect does changing the base of a logarithm have on its graph?

Back

Changing the base of a logarithm affects the steepness of the graph; larger bases result 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 x = b^y.

Front

How do you find the x-intercept of a logarithmic function?

Back

To find the x-intercept of y = log_b(x), set y = 0 and solve for x, which gives x = 1.

Front

What is the transformation of the graph y = log_b(x - h)?

Back

The graph y = log_b(x - h) is shifted h units to the right.