Tap or click on cards to flip them and reveal the answers. You can use arrow keys as well.
Loading folders...
1/15 cards
What is a logarithmic function?
Click to flip
A logarithmic function is the inverse of an exponential function, typically expressed as y = log_b(x), where b is the base.
Click to flip
How does the base of a logarithm affect the graph of a logarithmic function?
Click to flip
The base determines the rate at which the function grows. A larger base results in a more gradual slope, while a smaller base results in a steeper slope.
Click to flip
What is the domain of a logarithmic function?
Click to flip
The domain of a logarithmic function is all positive real numbers (x > 0).
Click to flip
What is the range of a logarithmic function?
Click to flip
The range of a logarithmic function is all real numbers.
Click to flip
Describe the general shape of the graph of a logarithmic function.
Click to flip
The graph of a logarithmic function is a curve that passes through the point (1,0), rises to the right, and approaches the y-axis but never touches it.
Click to flip
What is the vertical asymptote of a logarithmic function?
Click to flip
The vertical asymptote of a logarithmic function is at x = 0.
Click to flip
How do you find the x-intercept of a logarithmic function y = log_b(x)?
Click to flip
The x-intercept is found by setting y = 0, thus x = 1, because log_b(1) = 0 for any base b.
Click to flip
What happens to the graph of a logarithmic function if the base b > 1?
Click to flip
If b > 1, the function is increasing, meaning it rises as x increases.
Click to flip
What happens to the graph of a logarithmic function if 0 < b < 1?
Click to flip
If 0 < b < 1, the function is decreasing, meaning it falls as x increases.
Click to flip
What is the inverse operation of a logarithmic function?
Click to flip
The inverse operation is an exponential function.
Click to flip
Why can't the base of a logarithm be 1?
Click to flip
If the base were 1, the log function would be undefined for all x ≠ 1, as log_1(x) isn't defined in a meaningful way.
Click to flip
How is the change of base formula used in logarithmic functions?
Click to flip
The change of base formula, log_b(x) = log_k(x) / log_k(b), allows you to compute a logarithm using any base k.
Click to flip
What is the reflection property of logarithmic functions?
Click to flip
A logarithmic function y = log_b(x) is symmetric with respect to the line y = x when compared to its inverse, the exponential function.
Click to flip
How does a vertical shift affect the graph of a logarithmic function?
Click to flip
A vertical shift translates the graph up or down. For example, y = log_b(x) + c shifts the graph c units up if c is positive.
Click to flip
How does a horizontal shift affect the graph of a logarithmic function?
Click to flip
A horizontal shift translates the graph left or right. For example, y = log_b(x - h) shifts the graph h units to the right.
Click to flip
Need More Study Materials?
Go back to the chat to generate additional resources.