Question

Using complete sentences, explain the characteristics and parts of a logarithmic function and its graph.

Answer 1

Most logarithmic graphs resemble this same shape.
This graph is very, very close to the y-axis but does not cross it. The graph increases as it progresses to the right

In a straight line, the "rate of change" remains the same across the graph. In these graphs, the "rate of change" increases or decreases across the graphs.


Such logarithmic graphs of the form have certain characteristics in common:
Logarithmic functions are one-to-one functions. • graph crosses the x-axis at (1, 0)
• when b > 1, the graph increases

• when 0 < b < 1, the graph decreases

• the domain is all positive real numbers (never zero)

• the range is all real numbers

• graph passes the vertical line test - it is a function

• graph passes the horizontal line test - its inverse is also a function.

• graph is asymptotic to the y-axis - gets very, very close to the y-axis but does not touch it or cross it.




The function defined by

is called the natural logarithmic function.

(e is an irrational number, approximately 2.71828183, named after the 18th century Swiss mathematician, Leonhard Euler .)

Notice how the characteristics of this graph are similar to those seen above.

This function is simply a "version" of
where b >1.



Inverse of :

Since is a one-to-one function, we know that its inverse will also be a function.

When we graph the inverse of the natural logarithmic function, we notice that we obtain the natural exponential function, f (x) = ex.

Notice how (1,0) from y = ln x becomes (0,1) for f (x) = ex. The coordinates switch places between a graph and its inverse.

Answer 2

thats what it says in my old notes