4.3 Graphing Logs

Front

What is the domain of the logarithmic function?

Back

(1, ∞)

Front

What is the x-intercept of the function \( \log_7(x) \)?

Back

(1, 0)

Front

How are exponential functions and logarithmic functions related?

Back

They are inverses of each other.

Front

What is the range of the logarithmic function?

Back

(-∞, ∞)

Front

What does the transformation \( k(x) = \log(x - 6) - 4 \) represent in relation to the parent function \( f(x) = \log(x) \)?

Back

It has been shifted 6 units to the right and 4 units down.

Front

What is the general shape of the graph of a logarithmic function?

Back

It increases slowly and approaches the vertical asymptote at the y-axis.

Front

What is the vertical asymptote of the logarithmic function \( \log(x) \)?

Back

x = 0.

Front

What happens to the value of \( \log(x) \) as x approaches 0 from the right?

Back

It approaches -∞.

Front

What is the value of \( \log(1) \)?

Back

0.

Front

How does the base of a logarithm affect its graph?

Back

A larger base results in a steeper graph, while a smaller base results in a flatter graph.