Graphing Logarithmic Functions

For the function $f(x) = \log_b(ax + c) + d$, what transformation does the 'd' value represent?

The domain of a logarithmic function $f(x) = \log_b(x)$ includes all real numbers.

Describe how the graph of $y = \log_2(x)$ is transformed to obtain the graph of $y = \log_2(x - 3) + 2$.

The vertical asymptote of the function $f(x) = \log_b(x - h)$ is $x = $ ______.

Match each logarithmic function transformation with its corresponding effect on the graph:

Which of the following describes the range of a logarithmic function of the form $f(x) = \log_b(x)$, where $b > 0$ and $b \neq 1$?

The graph of $y = -\log_2(x)$ is a reflection of the graph $y = \log_2(x)$ across the y-axis.

What is the vertical asymptote of the function $f(x) = \log(x + 5)$?

The domain of the function $f(x) = \log_2(x - 4)$ is $x >$ ______.

Match the logarithmic function with its corresponding vertical asymptote:

How does the graph of $f(x) = \log_2(4x)$ compare to the graph of $f(x) = \log_2(x)$?

If $f(x) = \log_b(x)$ and $g(x) = b^x$, then $f(g(x)) = x$ for all real numbers x.

Describe the end behavior of the function $f(x) = \log_2(x)$ as $x$ approaches infinity.

The function $f(x) = \log_5(x)$ is ______ over its entire domain.

Match each logarithmic function with its corresponding transformation compared to the parent function $y = \log_2(x)$:

What is the effect of changing the base from 2 to 10 in a logarithmic function, such as comparing $f(x) = \log_2(x)$ to $g(x) = \log_{10}(x)$?

The graph of $y = \log_b(x)$ always passes through the point (0, 1) for any base $b > 0$ and $b \neq 1$.

For $f(x) = \log_3(x)$, find the value of $x$ when $f(x) = 2$.

The range of the function $f(x) = \log(x^2 + 1)$ is $y \geq$ ______.

Match each function with its corresponding description: