How do you describe the transformation of a logarithmic function?

Recall the general form of a logarithmic function is: f ( x ) = k + a log b ⁡ where a, b, k, and h are real numbers such that b is a positive number ≠ 1, and x – h > 0. A logarithmic function is transformed into the equation: f ( x ) = 4 + 3 log ⁡ .

How do transformations affect the logarithmic graph?

By adding or subtracting numbers from the logarithm equation or argument, you will shift the graph of the logarithm up, down, left or right. It’s easy to do if you remember the rules of transformation. If the transformation is to the left or right, it will affect the domain of the graph but not the range.

What is a transformation of a logarithmic or exponential?

The transformation of functions includes the shifting, stretching, and reflecting of their graph. The same rules apply when transforming logarithmic and exponential functions.

How does the base of a log affect the graph?

From this analysis, it can be concluded that as the base of a logarithmic function increases, the graph approaches the asymptote of x = 0 quicker. Also, the function may increase at a slower rate as the base increases.

Is Antilog the same as ln?

Ln is not an antilog, it is instead the natural logarithm, that is the logarithm with a base of e, the exponential function. An antilog is the reverse of logarithm, found by raising a logarithm to its base.

Does the order of the transformations matter?

The order does not matter. Algebraically we have y=12f(x3). Of our four transformations, (1) and (3) are in the x direction while (2) and (4) are in the y direction. The order matters whenever we combine a stretch and a translation in the same direction.

What is the antiderivative of ln x?

What is the antiderivative of ln x? The integral (antiderivative) of lnx is an interesting one, because the process to find it is not what you’d expect. Where u and v are functions of x. = xlnx −x + C → (don’t forget the constant of integration!)

How do you transform a graph of a function?

The transformation of functions includes the shifting, stretching, and reflecting of their graph. The same rules apply when transforming logarithmic and exponential functions. Suppose c > 0. To obtain the graph of: Example: The graph below depicts g (x) = ln (x) and a function, f (x), that is the result of a transformation on ln (x).

How do you find the integral of LNX?

The integral (antiderivative) of lnx is an interesting one, because the process to find it is not what you’d expect. Where u and v are functions of x. = xlnx −x + C → (don’t forget the constant of integration!)

What is the transformation of exponential and logarithmic functions?

Transformation of Exponential and Logarithmic Functions The transformation of functions includes the shifting, stretching, and reflecting of their graph. The same rules apply when transforming logarithmic and exponential functions. Vertical and Horizontal Shifts