A logarithmic function is the inverse of an exponential function, typically expressed as y = log_b(x), where b is the base.
A function that calculates interest over time.
A function that determines the height of an object in free fall.
A type of polynomial function with constants.
It doesn't affect the graph at all.
It shifts the graph vertically.
It rotates the graph around the origin.
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.
The domain of a logarithmic function is all positive real numbers (x > 0).
The domain is all non-negative real numbers.
The domain includes all real numbers.
The domain is all integers greater than zero.
The range of a logarithmic function is all real numbers.
The range is all positive real numbers.
The range is all integers.
The range is limited between 0 and 1.
It's a straight line that increases indefinitely.
It forms a perfect semicircle.
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.
It is an upward parabola.
The vertical asymptote of a logarithmic function is at x = 0.
It has no vertical asymptote.
The vertical asymptote is at y = 0.
The asymptote is determined by the exponent.
Set the base b equal to zero.
There is no x-intercept for a logarithmic function.
The x-intercept is found by setting y = 0, thus x = 1, because log_b(1) = 0 for any base b.
The x-intercept is at x = -1.
If b > 1, the function is increasing, meaning it rises as x increases.
The graph becomes a flat line.
If b > 1, the function decreases as x increases.
The function becomes undefined.
If 0 < b < 1, the function is decreasing, meaning it falls as x increases.
The graph becomes a parabola.
The graph flattens out and rises to infinity.
It increases exponentially.
The inverse operation is an exponential function.
The inverse is an arithmetic function.
The inverse is a square root function.
The inverse is a polynomial function.
The base can be 1, it just changes the graph.
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.
1 is too small to serve as a base.
It simplifies directly to a linear function.
It helps to create new bases from existing ones.
The formula applies only to base 10 logarithms.
The change of base formula, log_b(x) = log_k(x) / log_k(b), allows you to compute a logarithm using any base k.
It adjusts the graph for different scales.
A logarithmic function y = log_b(x) is symmetric with respect to the line y = x when compared to its inverse, the exponential function.
The graph reflects over the y-axis in all cases.
It reflects horizontally across y = 0.
It reflects over its own x-intercept.
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.
It rotates the graph 90 degrees.
Vertical shifts have no effect on the graph.
It only changes the slope.
A horizontal shift stretches the graph reset.
A horizontal shift translates the graph left or right. For example, y = log_b(x - h) shifts the graph h units to the right.
Horizontal shifts mirror the graph around the y-axis.
It doesn't affect logarithmic functions.