What can you say about the end behavior of the function [tex]f(x) = log_{10} (5x-1)[/tex]?

A. One end decreased and one end approaches a constant
B. One end increase and one end decreases
C. Both ends increase
D. Both ends decrease

Respuesta :

Answer:

C. Both ends increase

Step-by-step explanation:

The end behavior of a function can be evaluated using limits by letting the independent variable x approach positive or negative infinity. An alternative to this approach is the graphical method. We graph the function, then study it's characteristics and then determine its end behavior.

We can graph the given function using graphing utilities, Desmos graphing being the most common and preferred graphing tool for its ease of use. The graph of the function as obtained from desmos graphing tool is shown in the attachment below.

From the graph, the function increases in the interval [0.4, ∞) since the y values keep getting bigger. Nevertheless, the function is also increasing on the interval (0.2, 0.4]. The value of y when x = 0.2 is a point of discontinuity.

Ver imagen Hulkk